For residents, New York is a city of neighborhoods

Popular wisdom has it that New York is a wonderful place to visit but a terrible place to live. For a great many people, however, the opposite is true. Within a few minute's walk, a New Yorker can choose from an incredible variety of shops, markets, movies, and restaurants. Decisions to go to the theater, to the opera or ballet, to a classical concert or recital, can be made on the spur of the moment. Fine museums, first-rate schools, major sporting events, the best jazz, rock, or pop entertainment, can all be had without ever getting into a car.

The visitor, on the other hand, finds himself in an overwhelming welter of speeding taxis, pushing crowds, and undecipherable subways. It's no surprise that many people leave New York wondering why anyone would ever live there by choice.

What they may not understand is that New York is a city of neighborhoods, areas defined by their ethnic group or economic status, and that most New Yorkers identify first with their neighborhood and second with the city.

These communities are the real New York, ignored by tour buses and far removed from midtown hotels and the seediness of Times Square. Exploring them on foot, one discovers the diversity, the energy and excitement, that explain why, for so many, New York is home. Columbus Avenue and the Upper West Side

A decade ago, Columbus Avenue in the 70s was bordered by run-down apartment buildings and decaying brownstones. Then, as so often happens in New York, someone had the audacity to open a restaurant in one of the worst sections of town. It was a huge success, and now Columbus Avenue between 86th Street and Lincoln Center boasts fashionable clothing stores, art galleries, and innumerable restaurants and gourmet shops.

On weekends, the residents take to the streets, turning the area into an urban parade. A good place to join it is at D. D. L. Food Show on 81st Street. The latest production of movie mogul Dino De Laurentiis, it is an extravaganza of brass, brick, tile, and wood separated into specialty departments.

One of the nicest ways to spend a New York afternoon is to stroll down Columbus Avenue, perhaps visiting the Museum of Natural History at 79th Street, to browse leisurely in the shops, then to dine at the Ginger Man, the Saloon, or O'Neal's Balloon, all in the low 60s, and finally to take in a concert, an opera , or ballet at Lincoln Center. The East Side

The East Side is separated from the Upper West Side by Central Park, and everything that Columbus Avenue is - young, brash, highly visible - the East Side is not. Fifth, Madison, and Park Avenues in the 60s, 70s, and 80s exude tradition, stability, good taste, and, above all, money. In addition to galleries, fine shops, and salons, the East Side contains the city's most elegant town houses, some of which are now private schools or foreign embassies, many still homes of the wealthy.

The most splendid of these mansions was built in 1914 at Fifth Avenue and 70 th Street for the industrialist Henry Clay Frick. In it he hung Rembrandts, Titians, and Turners and now his collection, and his home, are open to the public. Unlike its great neighbor, the Metropolitan, at 82nd Street, the Frick is a museum that can be enjoyed without leaving the visitor exhausted.

Madison Avenue is pure commerce, albeit of a highly refined variety. If you should need something to brighten that dark corner of the living room, Len and Gerry Trent at No. 950 will sell you a Tiffany lamp for $42,000. Perhaps you are in the market for an old master drawing or some French Impressionists. At Knoedler Gallery on 70th Street, there's a good chance that you will find what you want.

From 77th Street south, Madison Avenue is art, antiques, crafts, and the Whitney Museum near 74th, with its fine collection of 20th-century American paintings and sculpture. Toward the 60s the galleries thin out, and expensive boutiques take their place. The Lower East Side

Eighty years ago, the Lower East Side was a slum teeming with impoverished Jews from the shtetlach of Eastern Europe and Russia. Today it is where New Yorkers go to shop for bargains. The tenements are still there, reminders of the days when beds were rented in shifts, to accommodate both day and night workers. Now the stores sell fashionable clothing, expensive appliances, and designer fabrics at the best prices in town. In spite of the changes, much of the flavor of the old neighborhood remains in the shops run by Hasidic Jews, the stalls selling chocolate egg creams, the clothing hung on outdoor racks.

Beginning at the Grand Street subway station, the stores immediately to the east sell linens, towels, and blankets. At Orchard Street, shops on the left feature inexpensive clothing, while those on the right sell better-quality merchandise, including designer jeans and leather jackets and coats. As one continues on Grand to Essex, the tempting smells wafting from the right signal the Pickleman's store with its barrels of red peppers, pickles, and sauerkraut standing open on the sidewalk.

The premier eating spot of the Lower East Side is Sammy's Roumanian, a warm, happy place that serves huge quantities of food redolent of garlic. It's at 157 Christie Street. Sammy's is closed Friday nights and Saturdays, as are all the local businesses, because of the Jewish Sabbath. The Ninth Avenue Market

The great migrations of the turn of the century consisted primarily of poor people, and they brought with them their hearty peasant cuisines. Often these included foods to be eaten by hand: Jewish knishes, Chinese egg rolls, and overstuffed Italian sandwiches. On Ninth Avenue near 37th Street is a store that has taken the tradition to ridiculous lengths. Manganaro's sells a custom-made, six-foot-long submarine sandwich, enough food to feed 30 to 40 people. They claim that it is a favorite at chic East Side parties.

At lunch hour, the store is filled with local workmen eating heroes of meatballs and sauce, veal and peppers, and other messy delights, while shoppers from uptown buy homemade mozzarella and Italian sausage at the groceria next door.

Manganaro's is in the heart of Italian Ninth Avenue, a street where immigrants opened fruit stands, butcher shops, and bakeries. Over the years, Greeks, Puerto Ricans, and Chinese have introduced markets of their own, and now the area is a cornucopia of exotic foods. Spices sold in little tin cans in supermarkets are displayed here in multicolored rows of open sacks. Dried cod, bacala, stands rigid against the walls. Sunday in Harlem

The largest of the new neighborhoods was fed not by foreigners, but by Americans from the Southern states, and it grew until it became a city within the city.

Harlem is a blend of Africa, the Caribbean, the deep South, and the city, a world-famous symbol of, variously, racial oppression, black pride, revolution, resignation, and hope. Like all stereotypes, these distort rather than reveal the truth, but for those who wish to see a bit of the real Harlem, a unique tour provides a brief exposure to the roots of black American music. Called the Harlem Spiritual Gospel Tour, it leaves from 166 West 46th Street on Sunday mornings for a ride through not only the slums of Harlem, but the upper-middle-class homes of Sugar Hill and Strivers Row.

It culminates with a church service at the First Corinthian Baptist Church, chosen because it expresses the exaltation of spirit that found a home in the black church. Here, among the warm and welcoming congregation, the visitor experiences an aspect of a culture that may be very different from his or her own.

Reservations for the tour, which costs $22, may be made by calling (212) 275- 1418. SoHo

Neighborhoods have a way of changing in New York, sometimes it seems, as in the case of Columbus Avenue, almost overnight. Others spring up where there had been no neighborhood before. One of these is known as SoHo, for ''south of Houston.'' Long a district of huge, cast-iron factories, it was discovered in the 1960s by artists who rented the vast open floors and converted them into low-cost living and working spaces. Inevitably, as the word spread, shops and galleries followed. Now the artists who discovered it cannot afford it.

In spite of the skyrocketing property values, the several-block-square area is a strange jumble of the renovated and the run-down: high-priced modern art, far-out fashions, trendy bars, and buildings still used for the manufacture of cardboard boxes.

Tourists and New Yorkers alike love SoHo, and flock to it on weekends, taking the subway to Prince or Spring Street, and the No. 5 bus to West Houston. They brunch at Tennessee Mountain and New Deal, or lunch on the fabulous salads at the SoHo Charcuterie, at Spring and Sullivan. They amble down West Broadway, the main street of this little town, gazing at the latest word in fashion, wondering at the current trends in art.

For art is what SoHo is still about. With all its flashiness, it is one of the major art centers of the world. The most powerful dealers, the most influential galleries, the work of the best contemporary artists, all come to SoHo.

And yet it is a real neighborhood. When the galleries and boutiques close and the narrow streets slowly empty, the artists and their families remain, in beautiful loft apartments they've created in the old factories. The West Village

Many of the artists who originally settled in SoHo were fleeing the high prices of Greenwich Village, a few blocks to the north. They took the paths of the writers of the '30s who made the Village a famous bohemian outpost and were followed by rebels of each succeeding generation.

They are coming yet, but much has changed. MacDougal and West Eighth Streets are tawdry and cheap. The area bordering 5th is lovely, genteel, and polite. The once-quiet streets near the Hudson River are experiencing a renaissance similar to SoHo's.

Only one small section holds on to the feeling of the real Village, and many consider it the best place to live in the city. Like the other neighborhoods, it has restaurants, galleries, and shops, but with a difference. Streets intersect at odd angles and stores are hidden in corners and basements. The houses are small, unpretentious, and very old. The pace of life is slower, and here, more than anywhere else, is it possible to escape the intensity that characterizes New York.

The West Village is bordered east and west by Seventh Avenue and Hudson Street, uptown by Jane and downtown by Morton. Within these several blocks one can wander at random and be perfectly content, but a possible starting point is West Fourth Street at the Sheridan Square subway station. Walk uptown to Bank Street, passing the lovely residential side streets, left to Bleecker with one antique shop after another, right on Christopher, another right on Hudson past the White Horse Tavern where Dylan Thomas used to hang out, and on to Abingdon Square and the uptown buses. It is a 17-block walk in the footsteps of countless Americans whose creative spirits were nurtured in these streets.

Here, then, are some of the neighborhoods of New York. There is much to see in them, but none of it obligatory. Instead, they are places to observe and enjoy the life of the city with those who live it every day.

To do so is to realize that New York is as varied as its people. Like them, it is tough and impatient. But like them also, it is creative, vibrant, and involved. It is this positive energy that many visitors miss, simply because they don't know where to look. New York's neigh