TRAVELING IN STYLE : Quartet of Quiet Quality : <i> Four fair and balmy havens bid you stay: Anguilla, Montserrat, Antigua and Jumby Bay</i> .

Elsewhere in the Caribbean, on more sophisticated, more developed islands such as Jamaica or Puerto Rico, sprawling high-rise resorts are crowded with tourists dressed, or almost dressed, in the latest couturier fashions. They work feverishly on tans, drink too many rum punches and stay up too late in the noisy nightclubs and discos. If this frenzied search for a good time appeals to you, skip the distinctive destinations that follow. They are not for you.

ANGUILLA

Anguilla (ann-GWILL-ah) is one of those delicious destinations to not-so-casually mention at a cocktail party in the competitive game of place- dropping. If you participate, be sure your pronunciation is accurate. Take your panegyric to an even loftier plateau and add the name Malliouhana (MAHL-ee-oh-HAH-nah) as in, “It’s the only place to stay when you go, dahling.” The rewarding part of this bit of pretentiousness is that you can rest assured that your suggestion is gospel. And the wisest decision you’ll ever make is to check it out yourself.

Almost within hailing distance of St. Martin, Anguilla has thus far offered little in the way of competition to the French/Dutch island only a 20-minute ferry ride away. Now, it is beginning to flex some impressive muscle.

A petite 3 by 16 miles, Anguilla has no golf course, no casinos, only two traffic lights (the second one went into operation a few months ago)--not even an authentic town. The largest settlement is The Valley, where a few shops and guest houses, a hospital and a police station huddle together.

However, you’ll be hard put to find lovelier beaches anywhere in the Caribbean: powdery white sand flecked with pink, and waters so clear you can see 50 feet down. Best of all, they’re relatively deserted.

Anguilla also has Malliouhana, a stunning, totally unexpected Moorish-West Indian palace heavily flavored with Caribbean and Cote d’Azur attributes and flanked by a pair of nonpareil beaches.

Entering its fourth full season, it is already popular enough to have been almost fully bespoken for during this past high season (December through March)--80% to 90% of that being repeat business.

The main building, spectacularly landscaped, offers 40-plus rooms and seven suites. There are seven more three-bedroom beach villas that can be divided into suites. And just completed last Thanksgiving are six additional junior suites that overlook the atolls of Prickley Pear and Dog Island.

Eight French chefs preside in the kitchens creating some of the most superb dining in the Caribbean. Joe Rostang--he of haute cuisine fame at La Bonne Auberge at Antibes on the French Riviera-- oversees the kitchens of the resort. The wine cellar stores at least 30,000 selected bottles.

Along the hillside, crowded with foliage and tropical flowers, are unexpected patios that overlook a sea so blue as to be almost artificial-looking, like an overdone but splendid watercolor.

At night, the ambiance of the main bar and lounge is pure Caribbean chic, illuminated mostly by candlelight and fanned with gently revolving ceiling fans.

Recreational facilities include a 35-foot powerboat that’s available for excursions and deep-sea fishing; three swimming pools, (one waterfall-fed), tennis courts and a water-sports center offering, well, everything. There are gift shops and a beauty salon, of course.

Leon Royden and his wife, Annette-- owners and managers of the Malliou- hana--orchestrate the activities of the 200 employees to top efficiency.

Understandably, It costs a little more to cultivate this certain holiday panache. A luxury double is $250 to $325 daily; a one-bedroom suite, $400 to $500 daily; the three-bedroom beach villas from $1,000 to $1,200 daily. Meals are extra, with dinner per person about $50 and up, without wine or cocktails. Rates are lower from May 1 until the end of August. The hotel is closed during September and October. Telephone (212) 696-1323 or (809) 497-6111.

MONTSERRAT

From the airy living room, across the spacious lanai, the aqua waters of your private swimming pool shimmer in the brilliant sunlight. Far below the villa perched high on the landscaped hillside, a catamaran curtsies gracefully over the waves that move in from the horizon to collapse in a billowing white froth on the black sands of a small beach.

Warm trade winds set the fronds of the palm trees in lazy motion and bring with them the fragrance of tropical flowers along with the salty scent of the sea.

Softly, the hi-fi plays the soothing strains of a ballad, and the ceiling fan whirs gently, blending the music, the sounds of the surf below and the special scents of this serene little island.

Montserrat, a mere 15 by 9 miles in size, is a tranquil, relatively undiscovered piece of the Caribbean that won’t remain that way long. It is still a perfect place to escape, to heal, to rest, to be restored, to love and be loved.

The Emerald Isle, as it’s called, bears a striking resemblance to rural Ireland with its lush rolling valleys, forested mountains and cultivated slopes dominated by Mt. Chance, a 3,500-foot dormant volcano. And the island people are as warm and hospitable and hardworking as their European counterparts.

Although only a 15-minute flight from Antigua, Montserrat, with fewer than 25,000 tourists a year, thus far has remained out of the mainstream of Caribbean traffic. Most of these are repeat visitors who return year after year to their favorite hotel, guest house or villa.

Newest and most spectacular in this last category are the Villas of Montserrat, three luxurious homes that are situated atop a high hill that overlooks the sea. Custom-designed to afford complete privacy, the villas, going into their second season, will accommodate up to six guests each. And all have three bedrooms, three baths (one with a whirlpool bath), a spacious living room with color TV and a stereo system, a telephone, a dining area and a gourmet kitchen equipped with microwave and dishwasher. (The complex also has its own washer-and-dryer facilities). They were built by Californian Bruce Fielding, who has had a home on the island for almost eight years.

Rates include air fare aboard a private plane from Antigua, five-day maid service, and pool and grounds maintenance. Arrangements can be made for a private cook.

As an arriving guest, you will be met in Antigua and assisted through immigration and customs, then escorted to a private aircraft for the 20-minute flight to Montserrat. Upon arrival, you will again be met, this time by Wilston (Pickett) Johnson, whose title is resident manager but whose talents are that of a concierge. Request what you will and Johnson will find a way to come through for you.

He’ll drive you to your own private villa, where a maid awaits to serve you chilled rum punches followed by a cold lobster-and-Champagne dinner prepared by the Belham Valley restaurant, one of the island’s finest.

Such service continues through the next morning, when you will be served breakfast on the patio and treated to a tour with Johnson to acquaint you with the island, assist you with a rental car, if you wish, and be sure that you have everything you need to make your villa stay perfect.

A cherished memory is watching the Caribbean sunsets from your patio. If the light is right, you’ll see the islands of Redonda, Nevis and perhaps St. Kitts in the distance as the dazzling performance of the sunset disappears into the sea. In the quiet of the evening, the lights of the small houses and shops of Old Town begin to appear, and the symphony of tree frogs and crickets begins its nightly concerto.

Island activities include golf on a 6,500-yard course, tennis, windsurfing, sailing, horseback riding, guided hiking and tours. And, if you really need discos, there are two that open on weekends. Dining on the island is excellent.

Winter rates (Dec. 15 to April 15): $1,650 per week for the first two weeks, $1,450 for each succeeding week. Summer rates: $1,360 for each of the first two weeks, $1,160 for each succeeding week. Rates are per villa.

For further information, contact Wilston (Pickett) Johnson, P.O. Box 421, Plymouth, Montserrat, West Indies, telephone (809) 491-5513, or Bruce Fielding, 444 Castro St., Room 400, Mountain View, Calif. 94041, telephone (415) 964-3498. For information on Montserrat, the Montserrat Department of Tourism, Tromson Monroe Inc., 40 East 49th St., New York, N.Y. 10017, telephone (212) 752-8660.

ANTIGUA

Alas, there is one minus to the process of getting to two excellent resorts in Antigua. It’s that too many Antiguans involved in the business of processing visitors to their islands are glaringly sullen. The Tourist Board should make them realize what a negative effect such a less-than-cordial attitude has on arriving tourists.

However, grit your teeth in dealing with customs and immigration--even with the island’s cabdrivers. Give as good as you get, and the reward can be Curtain Bluff, a five-star resort ensconced in a five-star setting, complete with windward and leeward beaches.

Owner Howard Hulford, a former pilot for Texaco, spotted the property from his plane more than 25 years ago. He astutely recognized its Shangri-La potential and could hardly wait to land and begin his dream of a resort extraordinaire . He has accomplished that goal and more. His home, built at the top of the bluff on the property, overlooks the incredibly blue-green sea and could be a setting for “Life Styles of the Rich and Famous.” He and his wife, Chella, entertain all the resort’s guests in their home weekly and are devout professionals and charming hosts.

The resort has been facetiously called “Camp Curtain Bluff” by some, but the comparison between it and Club Med, for instance, is akin to one between Tiffany’s and Woolworth’s. To ascertain that his dream remains the best , Hulford regularly pours money back into his resort, maintaining nothing less than excellence in accommodations, service, food and wine. More than $3 million was spent during the past two years to adhere to his rigid standards.

There are 49 double bed/sitting rooms, each with private terrace; six new one- and two-bedroom suites with spacious living rooms and private balconies, and large bedrooms--each with a sea-view terrace, marble bath and shower.

All rooms have his-and-her terry robes, a bidet, fresh flowers daily (grown in a nursery on the grounds), a wall safe and Spanish-marble floors, and all are beautifully decorated with wicker and soft pastels. The two-bedroom, two-level suites have a come-hither hammock strung invitingly on the trade-wind-cooled patio.

The Sugar Mill Bar is the gathering place for guests, and next to it are a living room-card room, a dining room and an outdoor dance floor where guests dance under the stars nightly to live music. As one guest observed, “This is a place where you fall in love with your wife all over again.”

No cut-off jeans in this establishment, please. Not even a $100 guayabera shirt will substitute for the jacket and tie required for men after sundown.

Recreational facilities include the two terrific beaches, four championship tennis courts, practice court, resident pro and pro shop. Proper attire is also requested on the courts. There’s water skiing, sunfish sailing, windsurfing, snorkeling and scuba diving. There’s a 48-foot yacht, Salaamat, awaiting the pleasure of guests, whether for cruising or deep-sea fishing.

Room service is available for all meals at no additional charge. Tipping is not permitted. Acceptance of gratuities by staff members is grounds for instant dismissal.

The kitchen has been under the auspices of chef Reudi Portmann for the past 22 years, and he prepares six entrees that change daily, four soups, and an embarrassment of desserts. An impressive wine cellar stores 25,000 bottles of the best, imported vintage selections.

Does all this work? Obviously. Some 80% to 90% of the guests repeat their visits yearly--some even more frequently. The 10-year guests receive a silver tray at a formal presentation during their stay, and 20-year guests (of whom there are 30) are rewarded with a gold tray. As for service, the ratio of help to guests is one to one.

For this splendid holiday, the daily rates from now to April 14 are $360 for a double room; one-bedroom suite, $550; two-bedroom suite, $990. Rates include breakfast and dinner. The resort is a member of the prestigious Relais et Chateaux. Telephone the latter’s New York office, (212) 289-8888, or the resort direct (809) 463-1115, (809) 463-1116 or (809) 463-1117. Rates are lower during the off season, Oct. 14 to Dec. 18 and April 15 to May 15. The resort is closed May 16 to Oct. 13. All rates are for double occupancy.

JUMBY BAY

Who of us hasn’t at least once in our lives dreamed of that perfect idyll--our own private tropical island? But consider for a moment: hauling in your own groceries, doing the cooking, laundry, cleaning . . . and you still have to take the garbage, well, if not out, somewhere .

Imagine instead the alternative of someone else’s private island, a roomy 300-acre paradise with a mere 28 rooms and a caring staff of 170 to see to your every need. Peace, privacy and the congenial ambiance of a house party with like-minded guests, if you wish.

No dream, this. It’s the description of Jumby Bay, which began life as a sugar plantation more than 200 years ago and has evolved into an exclusive hideaway just two miles north of Antigua.

Guests are ferried in by the island’s private launch after being handed a frosty rum punch for the 12-minute ride.

The property was premiered as a resort five years ago by Oregonian Homer Williams, who has since been joined in partnership by John and Harry Mariani, Villa Banfi vintners and importers.

Williams’ six original duplex “rondavels” have been added to with units at the Pond Bay House and a cluster of West Indian-style double-suite cottages. The 200-year-old Estate House has been completely restored and architecturally redesigned to serve as an inviting lounge, library and game room. Candlelight dinners are served here both indoors and outdoors on the patio. Dress is casually elegant in the evening, and men are not required to wear jackets or ties.

A handsome Beach Pavilion filled with glass tables, comfortable chairs and cushioned sofas is where most guests breakfast and lunch. Meals are prepared by chefs trained both in Europe and the United States, and entrees may be French, Italian and American, as well as of the native cuisine. Banfi wines, of course, are complimentary with all meals. Still another inviting lounge is available at the Pond Bay House.

In their rooms, guests find terry-cloth robes; a full complement of Jumby Bay’s own shampoos, lotions, etc.; wine, Antiguan rum and a selection of soft drinks. The rooms incorporate an abundance of wicker and rattan and have pleasant ceiling fans that augment the constant, balmy trade winds that breeze through the louvered windows.

A fleet of bicycles and an assortment of walking canes for hikers stand ready for those who wish to explore the island’s miles of trails. Three tennis courts provide further diversion. There’s snorkeling, scuba diving, sailing and windsurfing, or you may choose to forgo any of those and just plop down comfortably--with a book and a chilled island drink--into one of the many inviting hammocks.

Jumby Bay has a resident horticulturist for those who may wish to while away an hour or two learning about the lush foliage on the island, and a resident marine biologist, who will be happy to tell you about the hawksbill turtles that hatch their eggs on the island and are fiercely protected.

Though not a trace of it is evident, the island owners are in the process of building for sale a total of 65 villas on the island during the next five years, many of which will be available for rental when not occupied by their owners. The first of these, completed in December, was sold before work on it began. Prices for home sites range from $500,000 to $950,000, while villa prices vary from $600,000 to $1,500,000.

World War II landing-craft barges with three crew boats haul 500 people to work on the project seven days a week. But nary a sound carries to disturb guests. To buy on the island, one must be a club member, which means paying an annual fee of $60,000.

Daily rates for two for this island idyll now through April 3, $600; April 4-30, $475; May 1 to Sept. 8, $400. The resort is open November through Labor Day. Meals, wine and cocktails are included in the rates. The only extra charges are for day sailing, scuba diving and deep-sea fishing.

Jumby Bay, P.O. Box 243, Long Island, Antigua, West Indies, telephone (809) 462-6000, or Jumby Bay, 1111 Cedar Swamp Road, Old Brookville, N.Y. 11545, telephone (800) 437-0049, (516) 626-0600. In New York City, the number is (212) 819-9490.