A VISITOR TO New York attempting to sample the art scene in a short weekend will have to make some difficult choices. Perhaps the best way to approach the hundreds of galleries is to decide if you want to see traditional, contemporary or avant-garde art; that is, uptown, midtown or downtown.

In the art world, uptown is Madison Avenue, roughly the stretch between 57th and 82nd streets. Fifty-seventh Street itself is the midtown gallery area, on which stand many galleries stacked one on top of the other, east and west of Fifth Avenue; and downtown, the galleries are in Soho, the area "South of Houston" Street, and bounded by the Avenue of the Americas (Sixth Avenue) to the west, Canal Street to the south and Lafayette Street to the east.

An area of loft warehouses into which artists moved searching for large open spaces and low rents, Soho is now crammed with art galleries, restaurants and chic jewelry and clothing boutiques. It is exciting and fun to spend several hours or even a day there.

Saturday is the day--almost all the galleries are closed on Sunday--when you can visit the museums and auction houses. It would probably be wise to arrive Friday night to make the most of the weekend but be forewarned: You will be doing a lot of walking in New York and should wear comfortable, if fashionable, shoes.

Dressing for downtown gallery-going has become an art in itself, and watching the people is as much a part of the scene as viewing the exhibitions. For example, you should not wear a fur coat downtown, unless it is ankle-length or from an exotic animal (Downtown most of the fur coats are to be seen on men, uptown on women. And if you do wear a traditional fur coat in Soho, you will probably be seen as a tourist or eyed as a potential buyer.) UPTOWN

Begin on Saturday morning by visiting Madison Avenue and the galleries in town houses between Madison and Fifth avenues. This is the most relaxed yet dressed-up of the art scenes.

You might start with a gallery called La Boetie, at 9 E. 82nd St., just off Fifth Avenue, run by Helen Serger--one of the deans of the New York art world--and specializing in work of Russian and European artists from the teens, '20s and '30s. You will always see interesting work in this gallery, frequently drawings, small sculptures and even furniture. Another gallery with thought-provoking exhibitions, but usually of American artists, is Salander-O'Reilly, at 22 E. 80th St., off Fifth Avenue. There you walk through a series of rooms with drawings and paintings by Prendergast, Stuart Davis, Sheeler and Eakins.

Many galleries and private dealers each specialize in one area, so that people who are interested in American art may visit Salander-O'Reilly/Hirschl & Adler (21 E. 70th St.), Spanierman (50 E. 78th St.), Washburn (42 E. 57th St.), Kennedy (40 W. 57th St.) and Barbara Mathes 19 E. 71st St.), as well as the Whitney Museum (945 Madison Ave. at 75th Street) and the Museum of American Folk Art at 49 W. 53rd St.

If it is the haunting expressive works of Egon Schiele, the lyrical lines of Gustav Klimt, or the power of the German Expressionists that you are after, you will not want to miss the Sabarsky Gallery at 987 Madison Ave., between 76th and 77th streets, where an exhibition of work by Otto Dix is planned for April. German and Russian material is also to be found at Leonard Hutton (33 E. 74th St.) Dorothea Carus (872 Madison Ave., at 71st Street, the Galerie St. Etienne (24 W. 57th St.), Rachel Adler (58 E. 79th St.) and Rosa Esman (29 W. 57th St.), who will put together an exhibition of Russian avant-garde posters and books in the spring.

The venerable Wildenstein and Co. is an important stop in uptown gallery viewing. The beautiful exhibition spaces have a fine scale for the old-master and Impressionist paintings usually exhibited there, and you can also experience the distinctive flavor of an Old World art gallery, with its marble floors and hushed ambiance.

There are several galleries new to New York where you can also view old-master paintings and drawings; among them, the British firms of Noortman and Brod (1020 Madison Ave., at 78th Street) and Colnaghi (26 E. 80th St.) and the French firms Maurice Segoura (58 E. 79th St.) and Didier Aaron (32 E. 67th St.).

If you are interested in seeing works by the 20th-century European masters Picasso, Braque, Gris, Modigliani, Leger and Miro', you may choose to stop by the Perls Gallery, at 1016 Madison Ave., where there is a sidewalk created by Alexander Calder outside the building; Saidenberg Gallery, at 1018 Madison; or Acquavella, at 18 E. 79th St.

If you have chosen only a few uptown galleries, you should have the energy for a stop at 57th Street and a dash through Soho later in the afternoon. MIDTOWN

The Fuller Building, at 41 E. 57th St., is a focus for midtown viewing. The midtown scene is faster moving than uptown, although you will spend some time waiting for elevators. You can visit the gallery of Pierre Matisse, son of Henri Matisse, who represents Balthus and Miro' and shows the work of contemporary European artists. In the same building is a gallery new to New York, from Oslo, the Galleri Bellman, which opened with a huge exhibition of Edvard Munch and is currently showing paintings, drawings and prints by German Expressionists. It is a novelty to see labels with the asking prices of each work in this gallery.

Across the street are two galleries worth visiting and very different in style. One is the large Pace Gallery, on several floors at 32 E. 57th St., which recently held a comprehensive exhibition of Picasso sculpture from the artist's estate. The other is the Joan Washburn Gallery (42 E. 57th St.), now showing the paintings of Ilya Bolotowsky from the '40s and '50s in Washburn's intimate midtown space and Bolotowsky's work from 1979 to 1981 in her gallery in Soho, at 113 Greene St..

Galleries tend to acquire a particular character or ambiance from the selection of artists exhibited, the personality of the director and the flux of art movements. Through the years, the Sidney Janis Gallery, at 110 W. 57th St., has pioneered in the works of the 20th-century masters, from the Cubists and Surrealists to the abstract Expressionist painters, and is opening a show called "New Abstractions," the work of seven contemporary artists, which will run through March 5. Before leaving 57th Street, you should visit another representative gallery, Blum-Helman, at 20 W. 57th St., where you may see the work of artists whose reputations were established in the '60s and early '70s as well as contemporary patterned paintings and environments. DOWNTOWN

As you stroll into Soho, you'll suddenly encounter crowds of people on the streets. Your first stop should be the building at 420 W. Broadway. Take the elevator to the top floor and work your way down through the various galleries.

You cannot feel more a part of the art scene than when you're on the stairs at 420 W. Broadway. The much-discussed Mary Boone Gallery is on the ground floor and across the street. There will be a fashionable crowd and many foreigners gazing at the work of Julian Schnabel and David Salle. In the same building are the Castelli and Sonnabend galleries. Formerly husband and wife, Leo Castelli and Ileana Sonnagend frequently collaborate on exhibitions of such contemporary artists as Robert Rauschenberg and Robert Morris. Leo Castelli, one of the most notable figures of the modern art world, has three galleries--two downtown and one on 4 E. 77th St.--in addition to being a part owner of Castelli, Feigen and Corcoran on Madison Avenue.

In the Soho galleries, you will hardly ever see a label on the wall. An unobstructed view of the work greets you as you step inside each gallery, and you can usually see the entire exhibition at once. Rather than inviting contemplation, the open spaces and large works encourage a walk-around and the crowds a socializing that makes you very conscious of the relation of the people to the art.

Down the street, at 393 W. Broadway, is the Dia Art Foundation, with a permanent exhibition called the "Broken Kilometer" by Walter de Maria, which consists of 500 solid brass rods, each two meters long and laid end to end, almost filling the room. The impression of this shining floor is not unlike that of a high-tech Japanese garden.

At 383 W. Broadway is the O.K. Harris Gallery, usually exhibiting at least three shows at once, normally large canvases with Realist work, recently a large oil of fortune cookies and paintings after Monet's waterlilies. While you may think you are catching a glimpse of an incredibly realistic sculptural figure in the back room, it will probably be the ubiquitous proprietor himself, Ivan Karp, with his cigar, watching television.

One of the first dealers to brave the tundras of unchartered Soho is Paula Cooper, at 155 Wooster St., exhibiting the work of mature artists such as Jasper Johns, Brice Marden and Frank Stella.

A relative newcomer to Soho is The Drawing Center, at 137 Greene St., devoted to exhibitions of works on paper by contemporary artists. Last season The Drawing Center also had a fascinating show of sculptors' drawings, which included old-master and 19th-century works as well as modern work.

Greene Street is the newest gallery block in Soho. Leo Castelli has a space there (at 142 Greene St.), and there are several other galleries worth a visit in the same building, such as John Weber and Sperone Westwater Fischer.MUSEUMS

Sunday you may sleep a bit later than usual, since most of the museums do not open until 11 o'clock and the auction houses not until the afternoon. The "Museum Mile" is usually meant to include the area between the Museum of Modern Art, at 53rd Street off Fifth Avenue, to the Guggenheim Museum, at 89th and Fifth. However, there are many fascinating museums above and below these limits: from The Cloisters at Fort Tyron Park, housing the medieval treasures of the Metropolitan Museum in a reconstructed cloister where sacred music is played on Sundays, to the marvelous Pierpont Morgan Library, at 36th Street off Madison Avenue, with its exhibitions of master drawings and maunscripts.

One of my favorites is the Cooper-Hewitt Museum of Design, a part of the Smithsonian Institution, in the neo-Georgian Carnegie Mansion, designed in 1901 by Babb, Cook & Willard. The collection, at 2 E. 91st St., consists of textiles, wallpapers, drawings and metalwork, and there are always interesting special exhibitions, currently a show of designs for the theater.

The museums in New York are known for their architectural interest; most were built by famous architects or are housed in the original mansions where the collections were created. The Jewish Museum (92nd Street and Fifth Avenue) is the former residence of Felix M. Warburg and was designed in 1908 in the French Renaissance style. The Frick Collection, built in the same style in 1914, houses the collection of Henry Clay Frick. The Pierpont Morgan Library was designed by Charles McKim in 1906 in an Italian Renaissance style. The Solomon R. Guggenheim Museum was designed by Frank Lloyd Wright in 1959. It has always been controversial as an exhibition space. As a design, however, the building is spectacular, as you gaze up at the glass dome from the lobby or look across the ramps. The museum's collection is strong in the 20th-century masters, such as Miro', Chagall and Kandinsky.

The Metropolitan Museum of Art, at Fifth Avenue and 82nd Street, is the next stop downtown. You can spend the entire weekend at the Met and only sample the collections. So you will have to choose among the costume exhibition "La Belle Epoque," the new American Wing, the Temple of Dendur, the paintings collection and of course, the very important exhibition of the Vatican treasures, being shown for the first time outside Rome.

Another museum known for its architectural innovation is the Whitney Museum of American Art, 945 Madison Ave., at 75th Street. Designed by Marcel Breuer and Hamilton Smith in 1966, it houses, among the new acquisitions, the personal collection of the founder, Gertrude Vanderbilt Whitney, and large holdings of modern sculpture displayed in a sunken courtyard.

Don't miss the Frick Collection, 1 E. 70th St., the next stop downtown, if you enjoy seeing paintings, bronzes and enamels in the rooms in which they were first gathered. Among the masterpieces at the Frick are Rembrandt's "Polish Rider" and the Fragonard room with four panels created by the artist for Madame Du Barry.

The Museum of Modern Art, at 11 W. 53rd St., was designed by Philip Goodwin and Edward Durrell Stone. Its sculpture garden, designed by Philip Johnson in 1951, is crowded on weekends with people eating lunch in the outdoor restaurant and sitting on the steps overlooking Rodin's "Balzac" and Henry Moore's "Family Group." The Museum of Modern Art is internationally known for its collections, including masterpieces such as Van Gogh's "Starry Night" and Picasso's ground-breaking "Demoiselles d'Avignon."

Many auction houses are now open on Sundays, to accommodate the viewers wishing to see the rapidly changing exhibitions. The difference between these shows and those in the galleries and museums is that you may examine the objects and discuss them with the expert in charge of the sale. You might see Oriental rugs, toys and designs for the ballet and theater one week and English furniture, silver or books another.

It is fun to attend an auction, but don't bid if you are not sure of yourself. As the auctioneer's hammer comes down, you become the legal owner, Sotheby's has now moved its entire staff to the spacious modern building on York Avenue between 71st and 72nd Street. The spring season will feature free Sunday lectures, and sales of English furniture, silver and paintings to celebrate Britain Salutes New York in April as well as the very important, Impressionist paintings from the Estate of the late Mrs. Horace Havemeyer in May.

At the Christie's located at 502 Park Avenue at 59th Street, you can view Impressionist paintings, rugs and furniture. Photographs, costumes and toys are sold at Christie's East at 129 East 67th Street. Two other auction houses have interesting exhibitions and sales, but you should call to find out the times in advance. William Doyle at 175 East 87th Street, now has good paintings sales as well as furniture and Phillips, Son & Neale, the third British-run auction house, has moved to 79th Street off First Avenue.

The key to enjoying art viewing in New York is to select one or more geographical areas and topics of special interest to concentrate on, and return for at least another weekend!