ONE OF THE many advantages of spending your winter "island vacation on Manhattan is that getting there is relatively inexpensive.

Driving--for about four hours--is probably the cheapest way to go from Washington to New York, but if you elect that method be sure your hotel has garage facilities. Legal parking spaces are almost as scarce as haystacks in the Big Apple, and you don't want your sightseeing to include a trip to the impoundment lot.

Busing it may not be chic, but it's comparatively cheap: $47.75 for a round-trip 30-day excursion ticket on Greyhound (half for children 5--11), and through March 30, $36.20 on Trailways ($18.60 for children).

If you prefer to make tracks, avoid the Metroliner and take a regular Amtrak coach for $48 round-trip excursion fare. Be sure to check the time restrictions on excursion tickets and, if you're traveling with a spouse or other family members, ask for a family plan fare. The cost is about the same as an excursion ticket, but there are no time restrictions. If you take the Montrealer, which leaves Washington at 5:30 p.m., you can dine in one of the few remaining train dining cars.

If you want to fly, New York Air will take you there for $35 each way on weekends and a few weekday flights, and $55 on all remaining flights from Washington National Airport. (From Baltimore-Washington International Airport, the one-way fare drops to $25 on the evening flight.) The Eastern Airlines shuttle flights cost $35 one-way from noon Saturday to noon Sunday and $60 each way at all other times.

Once you get there, you have a wide choice of methods of getting around. Taxis, all of them metered, are more plentiful than in Washington -- but also more expensive. For long distances, it's especially economical to use bus or subway. Rides cost 75 cents no matter how far you travel -- even the 14 miles from the Battery to the Cloisters, for example. Buses require exact change.

The subway system can be dirty, crowded and, at night, dangerous. It's also fairly complex, so be sure you buy a transit system map (available at most stations) if you want to find your way around by subway.

On weekends, there are two "Culture Bus Loops" -- one that makes 22 stops at major attractions in midtown and uptown Manhattan and one that makes 32 stops at points of interest in downtown Manhattan and Brooklyn. Each costs $2.50 a day with free reboarding and buses running about every half hour. For further information, contact the NYC Transit Authority (212--330-1234).

New York is also a great walking city, since it's laid out on a fairly rational grid pattern. You can either buy a map or get one free by writing to the New York Convention & Visitors Bureau, 2 Columbus Circle, New York, N.Y. 10019. (As is the unfortunate case in almost every major city today, it's important to exercise caution when walking in certain areas and to stay out of others after dark, and it might be best for tourists to avoid some sections even in broad daylight. If in doubt, ask first.)

Whether walking or using public transportation, you won't be able to see everything in the Big Apple in a short stay. It's essential to plan ahead and focus your efforts on what interests you most.

If you're a first-timer, you can get a feeling for the city past and present by attending one of the hourly (seven days a week from morning until early evening) screenings of "The New York Experience." The multi-screen presentation costs $3.50 for adults, $1.75 for children under 12, and takes place in Rockefeller Center at McGraw-Hill Plaza, Avenue of the Americas and 49th Street (Phone: 869-0345).

While you're there, you might want to tour Rockefeller Center, a 17-acre complex of offices, shops, theaters and television and radio studios. You can wander around on your own or take a guided tour for $3.35 for adults, $2 for children. Tours begin every 45 minutes. Be sure to save some time to watch ice-skaters glide around under the giant statue of Prometheus by sculptor Paul Manship. Better still, rent a pair of skates and take to the ice yourself.

New York's other major sightseeing magnets include the Empire State Building (Fifth Avenue and 34th Street, daily 9:30 a.m. to midnight); The New York Stock Exchange (20 Broad Street, Monday to Friday 10 to 4); The Statue of Liberty (ferry leaves hourly 9 to 4 from Battery Park); the United Nations (First Avenue between 45th and 46th Streets, daily 9:15 to 4:45); and the World Trade Center with its Observation Deck (Church, Vesey, West and Liberty Streets, daily 9:30 to 9:30). All are open for tours.

If you've already seen -- or don't care about -- the major magnets, just pick a subject you're interested in. Art? There's oriental art at the Asia Society (725 Park Ave. at 70th Street) and at Japan House (333 E. 47th St.); medieval art at the Cloisters in Fort Tryon Park; design at the Cooper-Hewitt Museum (Fifth Avenue at 91st Street); Latin American Art at El Museo del Barrio (1230 Fifth Ave.); traditional European art at the Frick Collection (1 E. 70th St.); modern art at the Guggenheim (Fifth Avenue at 89th Street) and at the Whitney (Madison Avenue and 75th Street); and a little bit of everything at the Metropolitan (Fifth Avenue at 82nd Street), to name a few.

You could easily spend all day just at the Metropolitan, wandering through Egyptian temples, Chinese gardens and gazing at costumes of 18th century women, and in cold weather this may be an excellent plan. Brunch is served Saturdays beginning at 11 and Sundays beginning at 11:15.

Art is not limited to museums, of course. New York has hundreds of galleries where you can browse among contemporary art -- for free. Most galleries are on upper Madison Avenue between 72nd and 85th Street, along 56th Street just off Fifth Avenue, or in SoHo, an area of studios and galleries in cast iron buildings south of Houston Street near West Broadway. Shows are listed in local newspapers and magazines.

New York also offers every possible style of architecture -- from the Dutch-built Dyckman farm house at Broadway and 204th Street to the Gothic style Cathedral of St. John the Divine at Amsterdam Avenue and 112th Street to the modern Mies Van Der Rohe-Philip Johnson Seagram Building at 52nd Street and Park Avenue. Paul Goldberger's "The City Observed" Vintage Books, 1979, $7.95, is an excellent guide and walking tour companion to about 800 New York buildings.

New York practically invented modern theater, and you'll want to see at least one Broadway show while you're there. If you have your heart set on a particular show, write or phone for tickets well in advance of your visit. If you're willing to take a chance, visit TKTS -- the prototype of our own TICKETplace -- after 3 p.m. on the day you want to attend an evening performance (after noon for a matinee). Tickets to available shows are half-price at this kiosk at 47th Street and Broadway. You'll probably have to stand in line, which will give you a chance to take in all the sordid splendor of Times Square.

Inevitably you'll have to eat, and this necessity may be the highlight of your tour. Every kind of restaurant in every price range is available. You might, for example, take a nostalgia trip to the Automat. The only money-in-the-slot Automat left in the city -- and this one is actually a recreation -- is at 3rd Avenue and E. 42nd Street.

For a more elegant type of nostalgia trip, take the elevator to the 65th floor of the RCA Building in Rockefeller Center for dinner with a view in the '30s-style Rainbow Room. If you promise to leave by 8 p.m., you can have a four-course pre-theater dinner for $17.50. Or, join the New York beautiful people at chic little East Side holes-in-the-wall like Trastevere (309 E. 83rd St.), known for its calamare and its pasta.

You can combine cuisine and culture on your New York sojourn by eating ethnic -- in one of the city's many ethnic neighborhoods. Stroll the narrow streets of Chinatown (off Chatham Square south of Canal Street), browsing in the shops that sell everything from ginseng to sandals and visiting the Chinese Museum at 8 Mott St. Then stop for dim sum -- a Chinese lunch of hors d'oeuvres, sweet baked goods and tea that you choose from passing carts. Try the Nom Wah Tea Parlor at 13 Doyers St.

Just north of Canal Street lies Little Italy, a crowded neighborhood of homes, shops -- and Italian restaurants. A local institution since 1892 is Ferrara's, where you can loll for hours over cream-filled pastries and cappucino.

Another New York institution is Ratner's, a Jewish dairy restaurant at 138 Delancey Street in the heart of the Orthodox Jewish community on the Lower East Side. This is still an area of small Jewish-owned shops, specializing in low-priced clothing, dairy restaurants and cafeterias. It's well worth a weekend browse.

Yorkville, on the upper East Side around 86th Street and First Avenue, was once populated almost entirely by German immigrants. Today the population is more eclectic, but many good German and Eastern European bakeries and restaurants remain. Try the Kleine Konditorei at 234 E. 86th St. for apple strudel or for lunch or dinner. And while you're in Yorkville, walk over to the East River for a peek at Gracie Mansion, official home of the city's mayor