We New Yorkers know what you say about us -- that our city's a wonderful place to visit but that you wouldn't want to live here. And that's understandable. After all, no sooner do you arrive than you're thrust into an overwhelming welter of speeding taxicabs, pushing crowds and indecipherable subways. Your first, and perhaps only impression, is of dirt, noise and confusion. It's no surprise that many people leave New York wondering why anyone would live here by choice.

What you 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 secondly with the city. This attitude cuts the city down to size, makes it manageable, and the New Yorker becomes not just one of the anonymous millions but a member of a community with its own distinct personality.

Ignored by tour buses, far removed from midtown hotels and the seediness of Times Square, these communities are the real New York. Investigating them on foot -- the best way to see the city -- you can discover the diversity, energy and excitement that explains why, for so many, New York is home.

Here, then, are some of my favorite New York neighborhoods. 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.

Columbus Avenue and the Upper West Side A decade ago, Columbus Avenue in the 70s blocks was bordered by run-down apartment buildings and decaying brownstones. Then, as so often happens in New York, someone had the audacity to open an expensive restaurant in what was one of the worst sections of town. It was a huge success, the first of many, and now Columbus Avenue between 86th Street and Lincoln Center, in the low 60s, boasts fashionable clothing stores, art galleries, flower markets and innumerable restaurants and gourmet shops.

Symbolic of the area's new tone is the elegantly paneled Endicott Booksellers at No. 450 -- the kind of store you'd expect to find in London's Chelsea or the Parisian Left Bank. In fact, owner Encarnita Quinlan envisioned it as a private Victorian library where she could have the pleasure of putting a book in someone's hand and having them come back and tell her how much they enjoyed it. Readings by well-known authors are scheduled regularly. When I went to hear Gore Vidal, he decided he didn't want to read at all and led a lively discussion instead. It was a Columbus Avenue evening.

On weekends, the sidewalks here fill with an exotic melange of roller skaters in shorts, beautiful women in high-fashion casuals, street musicians and break dancers, dazed tourists, Hispanics and Asians, Indians and blacks. And for a view of yuppies on their home turf, Columbus Avenue is the place to be. They sit in outdoor cafes, crowd the shops and stop on street corners in clusters, greeting and laughing and flaunting their upward mobility.

One of the nicest ways to spend a New York afternoon is to join the crowd strolling down Columbus Avenue, browsing through shops and snacking on ice cream cones. In the evening, you can dine at any of the numerous restaurants along the way and, as a final treat, attend a concert, opera or ballet at Lincoln Center.

The Upper East Side The Upper 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. Madison, Park and Fifth avenues in the 60s, 70s and 80s blocks exude tradition, stability, good taste and, above all, money. In addition to galleries, posh shops and salons, the East Side contains the city's most elegant townhouses..

The most splendid of these mansions was built in 1914 at Fifth Avenue and 70th Street for the industrialist Henry Clay Frick. In it he hung Rembrandts, Titians, Turners and Corots, and now his collection and his home are open to the public. Unlike its great neighbor, the Metropolitan, on Fifth at 82nd Street, the Frick doesn't leave the visitor exhausted.

There are luxury apartments on Fifth and Park and handsome townhouses along the intersecting, tree-lined streets. In contrast, Madison Avenue is pure commerce, albeit of a highly refined variety. Here you can buy a Tiffany lamp for $42,000, or an Old Master drawing, or a painting by a French impressionist. The blocks between 77th and 75th streets contain the greatest concentration of galleries in the area.

If any one person and any one place typifies the Upper East Side ambience, it is Bobby Short and his Cafe Carlyle, at 35 E. 76th St. For 22 years, the song stylist has been entertaining the local gentry and their friends with his inexhaustible collection of the best pop tunes ever written. If you want to see where the rich and famous hang out, try the Cafe Carlyle.

From 77th Street south, Madison Avenue is art, antiques and crafts. At 75th Street is the Whitney Museum, with its fine collection of 20th-century American paintings and sculpture.

Toward the 60s the galleries thin out and expensive boutiques take their place. At 62nd Street, the atmosphere suddenly changes. Crowds are thicker, faster, more intense. These are office and business people, putting in their work time here but living somewhere else, and this is where the neighborhood ends.

The Lower East Side Eighty years ago, the Lower East Side was a slum teeming with impoverished Jews from the ghettos 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 people who worked days and nights, when children collected fruit wrappers for toilet paper and coal for kitchen stoves. Now the stores, where salesmen once grabbed customers off the streets, sell stylish clothing, expensive appliances and designer sheets and 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 and pretzels, the outdoor racks holding rows of clothing.

Beginning at the Grand Street subway station, the stores immediately to the east sell linens, towels and blankets. At Orchard Street, stores on the left feature inexpensive clothing, while those on the right sell more expensive merchandise, including designer jeans and leather jackets and coats. Farther along Grand on Essex, the tempting smells wafting from the right signal the Guss Pickle Emporium with its barrels of red peppers, pickles and sauerkraut standing open on the sidewalk.

If you saw the movie "Crossing Delancey," you'll recognize the green awning where the Hollywood hero sold his pickles. "They shot here four days," says the real owner of Guss Pickle, 28-year-old Tim Baker. Ask him if he plans on repeating the film's plot and he'll tell you, "There are plenty of girls around, but I'm not looking to get married."

In 1910, when Guss opened, there were 50 to 60 pickle stores on Essex. Now this is the only one left. As for the crucial question of what makes a real Jewish pickle: "It's like wine, the aging. They're naturally fermented in salt, water, garlic and spices -- four weeks for a half-sour, three months to a year for a sour."

On Canal, for two or three blocks to the right, appliances, watches, television sets and stereos are sold at discount prices. Another right on Christie returns you to the subway, while a few blocks farther on Canal are Chinatown and Little Italy.

The best eating establishment of the Lower East Side is Sammy's Roumanian at 157 Christie St. It's a warm, happy place that serves huge quantities of food high in cholesterol and redolent of garlic. Sammy's is open seven nights a week, unlike the many other local businesses that are closed on Saturdays in honor 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, overstuffed Italian sandwiches. At 488 Ninth Ave. near 37th Street is a store that has taken the tradition to extreme lengths. Manganaro's sells custom-made, six-foot-long submarine sandwiches, enough to feed 30 to 40 people.

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

Manganaro's is in the heart of Ninth Avenue, a street where early Italian 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 that are sold in little tin cans in supermarkets are displayed here in multicolored rows of open sacks. Dried cod, or baccala, stands rigid against the walls. At the Washington Beef Co., 575 Ninth Ave. between 41st and 42nd streets, huge sides of beef hang on sliding hooks.

At 511 Ninth Ave. an awning announces the Supreme Macaroni Co. and Guido's Restaurant. I have a vivid recollection of walking into the store years ago to find a rooster strutting among the bins of food. Now, Thomas Scarola informs me that my memory deceives me. He should know: In those days, he lived above his grandfather's store and was awakened many mornings by that very same rooster, the pet of the Greek store owner next door.

"There was never a menu," Scarola tells me. "Whatever my grandfather decided to make that day, that's what everybody ate." Now, different kinds of pasta are exhibited in neat bins, and in the back, the little restaurant has been spruced up to meet the standards of the celebrities whose pictures hang on the walls. Reservations are necessary for dinner (212-564-8074), but the food is still good southern Italian.

The Ninth Avenue market extends into the 50s, but the essence of the old neighborhood is crammed into the three blocks between 37th and 40th streets. In this section, the rough peasant vitality -- unsophisticated, exuberant and alive -- still exists.

Sunday in Harlem The immigrants who poured into New York from Europe and Asia claimed parts of the city as their own and transformed them into urban replicas of the villages they left behind. Little Italy, the Lower East Side, Chinatown and Hell's Kitchen were enclaves that had in common their poverty and the desire to be rid of it. The largest of the new neighborhoods, however, was fed not by foreigners, but by Americans from 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 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. Run by Harlem Spirituals Inc. (212-302-2594), it leaves from 1457 Broadway at 42nd Street on Sunday mornings for a ride not only through the more run-down sections of Harlem but also by the mansions and townhouses of Sugar Hill, Hamilton Terrace and Striver's Row.

It stops at the home of Alexander Hamilton and the historic Morris-Jumel Mansion, the headquarters of Gen. George Washington, before culminating with an authentic Sunday morning service at a Baptist church, complete with spiritual and gospel singing by the choir.

Duke Ellington advised us to "Take the A Train" to Harlem, but another company renders that mode of transportation unnecessary. Harlem, Your Way! Tours Unlimited Inc. (212-866-6997) leads champagne jazz trips uptown, walking and biking excursions, visits to Harlem's brownstones and Sunday morning gospel tours; reservations are required.

SoHo Neighborhoods have a way of changing in New York -- sometimes seemingly overnight, as in the case of Columbus Avenue. Others spring up where there had been no neighborhood before. One of these is known as SoHo, for "south of Houston" (the street is pronounced HOUSE-tun). Long a district of huge factories, it was discovered in the '60s by artists, who rented the vast open floors and converted them into low-cost living and working spaces. Inevitably, shops, restaurants and galleries followed, and now many of the artists who discovered SoHo can no longer afford to live there.

In spite of skyrocketing property values, the 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.

When I'm in SoHo I like to stop at Back Pages (125 Greene St.), a long, narrow store crammed with such delightful artifacts as Victorian barber chairs, Coke machines from the Eisenhower era, authentic striped barber poles and an antiquated Esso gas pump. The walls are hung with moose heads and old-fashioned signs for Salada tea, Kodak film, 7-Up and something called Natural Chilean Soda.

But I go to look at the jukeboxes, those essential appliances that once adorned every self-respecting diner and soda shop in the land. Prices range from $9,500 to $28,000. The most popular jukebox ever made, according to owner Alan Luchnick, was the Wurlitzer 1015 of 1945 and '46. You remember, the one with the rotating color wheel and slowly rising bubbles. Today it goes for $14,500, but the price is expected to almost double in 10 years. Make your purchase now.

Tourists and New Yorkers alike love SoHo, and they flock to it on weekends, taking the subway to Prince or Spring Street, or the No. 5 bus to West Houston. Then 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 centers of the world. The most powerful dealers, the most influential galleries, the best contemporary artists -- all are here.

And yet it is a real neighborhood. When the galleries and boutiques close and the narrow streets slowly empty, turning dark and quiet between the looming buildings, artists and their families remain in the beautiful loft apartments they've created for themselves.

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: beatniks, hippies and flower children, American's romantic and disaffected youth.

They are coming still, but much has changed. MacDougal and West Eighth streets are brassy and cheap. The area bordering Fifth is lovely, but genteel and polite. The once quiet streets near the Hudson River are experiencing a renaissance similar to that in SoHo.

In one small section of the Village, streets intersect at odd angles and stores are hidden in corners and basements. The houses are small and unpretentious and very old. They have the special charm of something that has been lovingly used, not merely preserved. The pace of life is slower, and here, more than anywhere else, it is possible to escape the intensity that characterizes New York.

When I first chanced upon Chumley's Restaurant at 86 Bedford St. and fell in love with its shish kebab with peanut sauce and wild rice, I didn't know that the site had been chosen for a different kind of escape. With two entrances that are almost invisible from the street, it was deemed an ideal location for secret meetings when it was bought in 1926 by a member of the International Workers of the World. Two years later, Lee Chumley opened a restaurant and speakeasy; soon the dark, square room became a hangout for local leftists and writers, of which the Village has always had a surplus.

The wild-eyed radicals and police raids are gone, but the murky atmosphere remains. Chumley's is one-of-a-kind Greenwich Village haunt, but now my favorite dish is only served to cognoscenti who call and order in advance (212-675-4449).

The West Village is bordered east and west by Seventh Avenue and Hudson Street, uptown by Jane Street and downtown by Morton. Within these 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 along the way. Turn left again on Bleecker (where there's one antique shop after another), right on Christopher (the core of gay Greenwich Village), another right on Hudson (past the White Horse Tavern, where Dylan Thomas drank himself to death), then 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.

To walk the streets of the West Village -- or any New York neighborhood -- is to realize that the city 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 neighborhoods are a good place to start.

For more information, contact the New York Convention and Visitors Bureau Inc., 2 Columbus Circle, New York, N.Y. 10019, (212) 397-8222.

Robert Ragaini is a New York writer.