Great Getaways : Times Correspondents’ Course in Favorite Weekend Escapes : CAIRO

Parted by the Nile, graced with perhaps the best medieval Islamic architecture in the world and pulsing with 15 million people, Cairo is a fascinating city to visit. Alas, it is also one of the dirtiest and most overcrowded, most dogeared cities in the world. If you spend any length of time there, it’s nice, from time to time, to be able to get away from it all.

The trouble is that there are few restful hideaways close enough to Cairo to make a weekend trip possible, unless you go by air. Also, accommodations are often poor and unsanitary. But there is a place that is clean and comfortable and so close to Cairo that most Egyptians seem to have overlooked its merit as a weekend retreat. It is the famed Mena House hotel.

Located on the western fringe of Cairo, Mena House was created by the Khedive Ismail as a royal rest house for his guests when they visited the Pyramids, which are just a few feet away. Rebuilt and enlarged many times and now a state-owned hotel managed by Oberoi, Ltd., Mena House manages to retain much of its old grace. The main lobby in the old rest house is a catacomb of vaulted ceilings, archways and mashrabia , fretted Arabesque woodwork.

History haunts the place. Winston Churchill, Franklin D. Roosevelt and Chiang Kai-shek met here during World War II. When he was still the Prince of Wales, the Duke of Windsor caused a stir when he scaled the Great Pyramid to drive a golf ball off its peak.

These days, golfers have it easier; there is an 18-hole course. Other amenities include a pool, tennis courts, seven restaurants, and a nightclub where Fifi Abdu, one of Egypt’s most famous belly dancers, writhes every night except Friday. There are several stables nearby, and a favorite pastime of residents is to go riding in the desert as the sun sets over the pyramids.

The 524 rooms are large and comfortable. Booking well in advance is advisable if you want to stay in one of the 30 or so rooms in the old rest house that have a direct view of the pyramids. Most of the rooms are in a new, architecturally undistinguished annex, but all have either a balcony or a patio.

For those who wish to splurge, there are the wood-paneled Churchill and Montgomery suites, which boast gold fittings in the bathrooms, and terraces big enough to re-enact the battle of El Alamein, all for only $550 a night.

Mena House, Pyramids Road, Giza, Cairo. Telephone 855-444 or 857-999. Telex 92316 OBTHL UN. Cost: $76 per couple in the new wing, $88 in the old rest house , tax and service charges included.