D.C. Dining Without Budget Deficit : From museum cafeterias to quality fast-food, eating well in Washington doesn’t have to be expensive.

Our nation’s capital is one of the best family destinations in the world, although it can be an expensive city to eat in. Yet we’ve discovered a few ways to dine well, enjoy interesting food and even find restaurants that kids are likely to enjoy--all without spending a bundle.

First, most of the great free museums that line the National Mall contain inexpensive restaurants or cafes. Among the most popular is the Flight Line cafeteria in the Air & Space Museum. In a sunlit, glass pavilion at the western end of the huge museum, the cafeteria is a fast-food emporium featuring everything from pizza to hot sandwiches, along with a selection of salads. It would be hard to spend more than $7 per person. And there are ways to cut the bill below that. We saw a group of Cub Scouts arrive with their own fruit and sandwiches and just go through the line for drinks and a pizza.

For something a little more refined, The Wright Place restaurant on the upstairs balcony in the center of the cafeteria offers table service in a comfortable atmosphere, and we found the food to be quite good. Nicely charred salmon, still pink on the inside, was served with broccoli and French fries ($10.95). We also found Brunswick stew ($8.25), a specialty in nearby Brunswick County, Va., to be hearty enough for two. It was served with tasty corn muffins.

Another popular cafeteria is on the lower level of the East Building of the National Gallery of Art. A waterfall behind glass forms one wall of the Concourse Buffet, which offers a selection of salads, sandwiches and hot dishes that cost $4-$6. The Cascade Espresso Bar, near the entrance to the buffet, offers tea sandwiches and pastries along with espresso and cappuccino for about $5 per person. The Garden Cafe, at the center of the gallery’s West Building in a lovely fountain court, serves salads and sandwiches for $6-$9.

Our favorite museum restaurant is the Corcoran Cafe in the Corcoran Gallery, about a block east of the White House. Small tables are set in an area just to the left of the main entrance. Doric columns frame the space and 19th-Century marble busts look down from the walls. Twin lines of palm trees divide the room in thirds. The lunch menu includes Oriental sesame beef and North American wild rice salad for $7-$10. But we prefer a visit in the late afternoon for cappuccino ($2.75) and dessert, such as a moist carrot cake ($3.50) filled with raisins. The cafe excels at little touches. Loose tea is used in pots rather than tea bags. A slice of lemon is served with a tiny clove. Even the carrot cake is served with a slice of raw carrot and a sprig of fresh mint.

If you find yourself away from the Mall and major galleries, head for Kramer Books near Dupont Circle--a pleasant neighborhood of restaurants, shops and graceful period homes. The afterwords cafe is shoehorned into a small space at the rear of the popular bookstore. A tiny bar serves drinks and food behind a rack of books to the left. More tables are in the rear and on a balcony above. There is a solarium in the back with still more tables. We opted for the balcony and a view of browsers among the book racks below.

The emphasis is on fresh ingredients and healthy eating. We couldn’t resist ordering the beef relleno pie ($9.75). What emerged from the kitchen was a casserole with chunks of tender beef and mild green chiles topped with a fluffy cornmeal topping. A small salad of lettuce, carrots, tomatoes and watercress, along with a spicy mound of black beans, completed the dish. Also a success was grilled vegetable lasagna ($9.75). Wide strips of pasta were rolled around pieces of zucchini, red pepper, potato and big leaves of fresh tarragon, mixed with ricotta cheese and topped by a light tomato cream sauce.

For dessert we tried the hazelnut tart: whole hazelnuts in a slightly sweet pie filling, and some of the best Key lime pie we’ve ever tasted.

Another place for affordable feasting is the beautifully restored Union Station. With trains arriving and departing, there is a bustle of excitement. We saw lots of families and teen-agers heading one level below the main floor, where there are more than 30 separate food stalls selling everything from Asian specialties to old-fashioned doughnuts.

At Flamer’s hamburgers, a cheeseburger costs just $3.55 and is grilled to order. We also liked the pizza at Mamma Ilardo’s, a branch of the popular Baltimore pizza parlor. The stand serves thick ($2.35) or thin ($2.15) pizza slices with a variety of toppings. Next door at Pure Sunshine, freshly squeezed lemonade is served, shaken like a martini. We also found stands serving fried chicken, sushi, barbecued ribs and hot dogs. Tables and chairs set beneath brightly colored umbrellas make it a cheerful place to eat.

Upstairs, America awaits. On a series of balconies above the main lobby at Union Station in what was formerly the men’s room and shoeshine parlor, the restaurant America serves dishes from around the country. Although more expensive than a fast-food outlet, America is perfect if you find yourself longing for a more complete meal at an affordable price. Portions are large. Mom’s meatloaf ($8.95) arrived on a plate with emerald-green broccoli and a huge pile of fluffy mashed potatoes. Two large slices of meatloaf occupied the rest of the plate. Unfortunately, the gravy was flavorless.

Much more successful was the Santa Fe Club sandwich ($8.50). A large round of chewy Indian fry bread was folded around a smoky grilled chicken breast with lettuce, fresh tomato and a slightly piquant guacamole. A salsa made from roasted peppers was a spicy accompaniment, and thick-cut but crispy French fries and fresh, tangy coleslaw completed the dish.

Death by chocolate ($3.95) and two forks made for a nice finish. The rich chocolate cake had a mousselike filling, a firm fudge topping, some drizzles of chocolate sauce and lots of whipped cream. Delicious, but too rich for one person.

The tour of the White House is still one of the most popular things to do in Washington, and we found the perfect way to recuperate from standing in the long lines: afternoon tea at The Carlton, a Washington landmark hotel built in 1926, just a short walk away. There you might even see a famous politician heading for the basement and a haircut with the President’s barber, Milton Pitts.

Afternoon tea in the ornate lobby with sunlight streaming through the tall windows and the lilting music of a harp in the background is a perfect way to end a Washington day of sightseeing. A complete tea with sandwiches, scones, Devonshire cream and pastries is $12.50. We noticed several families, with young children on their best behavior, enjoying the experience.

GUIDEBOOK

Cheap Eats

in the Capital

Recommended: Flight Line cafeteria and The Wright Place, National Air & Space Museum, 6th Street and Independence Avenue, S.W.; (202) 357-1300.

Concourse Buffet, National Gallery of Art, 4th Street and Constitution Avenue, N.W.; (202) 737-4215.

Corcoran Cafe, Corcoran Gallery of Art, 17th Street and New York Avenue, N.W.; (202) 638-3211.

Afterwords, Kramer Books, 1517 Connecticut Ave., N.W.; (202) 387-1400.

Union Station, 50 Massachusetts Ave., N.E.; (202) 371-9441. America restaurant, (202) 682-9555.

The Carlton, 923 16th St., N.W.; (202) 638-2626.