VIOLINIST Nadja Salerno-Sonnenberg plays Beethoven beautifully--but some days she would rather be playing left field in Central Park.

"I'm the best leftfielder," she was saying a few days ago, over lox and bagels in a coffee shop near Lincoln Center. "I'm as good as Dave Winfield . . . don't print that, he may think I really mean it. I'm not as good as Dave Winfield, but I'm good."

No critic has commented on her play in left field, but they have gone wild over her violin-playing. "Everything she did was absolutely right," said William Zakariasen of the New York Daily News a few months ago. "One shudders to think what she will play like in another 10 years." In the New York Times, John Rockwell found her playing "a model of refined, violinistic poetry," and in the Los Angeles Times, Martin Bernheimer rhapsodized about her "infinitely gentle, singing Mozart, suave, sweet, muted, yet capable of glitter . . ."

At 22, barely out of the Juilliard School and honored with a Naumburg Award, Salerno-Sonnenberg is just beginning a career that seems to have unlimited potential. Tonight, she plays at the Kennedy Center with the Mostly Mozart Festival, a prestigious showcase where she will be sharing the spotlight with well-established young stars such as pianist Emanuel Ax and cellist Yo-Yo Ma.

In recent months, she has been wrestling with image. Her early concerts, after she won the Naumburg Award, provoked enthusiastic reviews but reservations about her appearance; her hair was all over the place, out of control; her dress looked as if it had been bought at a garage sale (it had) and she needed coaching on such fine points as how to walk across a stage. Before waxing lyrical about her Mozart, Bernheimer had dutifully noted that "she strode onstage like a rather gawky teen-ager."

She gets advice: "They tell me, 'You gotta look nice when you go out. You don't want to come into Juilliard wearing pants with holes in them,' which I never really thought a very serious matter. It doesn't make sense in one way, but in another it does.

"In the last few months, I've had some help about fashion, what to wear, makeup. I've had my hair cut because I had a lot of complaints about how it was always in the way. Just recently, I went and bought a gown at Saks, which to me is such a waste of money: $255 for a gown and I could buy it for $5 at a garage sale. But it's a beautiful gown; it's very tight and it's black and I like it; I have to admit I like it.

"But $255. I could have bought a Yankees subscription with that.

"Everybody wants me to go around as though I were made of porcelain," she is saying, "but I couldn't. It's so much fun going to the park and playing softball. Why should I give that up? I hurt my shoulder, sure, but so what? We play football in the winter; I try not to play, but sometimes I can't resist."

She has given up auto-racing, partly for reasons of safety and partly in memory of a lost friend: "I used to race cars, but I stopped because a good friend of mine died recently. Have you ever had Mo et et Chandon champagne? Well, the son, Olivier Chandon, died recently. It was just amateur racing, but you have to take a test. I have a license she produces it but I don't do it any more, in homage to him."

Nadja Salerno-Sonnenberg was born in Rome, to a mother who was a pianist and a father who was a singer. "My father is Russian," she says, "but I don't know anything about him. He left when I was 3 months old. I wonder sometimes if he comes to my concerts." She began studying the violin when she was 5 with a member of the Italian Radio Orchestra and moved to the United States (New Jersey) with her whole family (mother, stepfather, brother and grandparents) on the advice of her violin teacher, who did not think she could get the kind of instruction she needed in Italy. She entered Curtis Institute in Philadelphia when she was 8, the youngest student there.

There are no tuition fees at Curtis; the only way you can get into the school is by being very good. But even without that kind of expense, times were hard for the Salerno-Sonnenberg family. "Garage sales," she recalls, "that's New Jersey. That's a way of life for me. They don't have them here in Manhattan; who has a garage? But in New Jersey, my mother would go every Saturday, every Sunday, and until I was 18 or 19, I wore only garage sale clothes. It's a great deal, you know. I wore garage sale gowns, dreses, everything. We're not very rich, and that's a good way to handle it."

She "first began to take the violin seriously," she says, when she entered the Naumburg Competition. The process sent her into a sort of tailspin that she describes in terms of food: "I went through a phase where I ate a half-gallon of Baskin-Robbins peanut-butter-and-chocolate ice cream every day. That was when I was preparing for the Naumburg--two months. I was manic; something wrong with me."

Still, she lost eight pounds in five days during the competition. After winning, she says, "everything turned around; all of a sudden, as much as I wanted to, as much as I fought it, I could not just consider myself a student any more. I was out there, and since I can't stand second-best, I just had to go for everything. I'm glad; I needed that kick in the a--, I'm such a lazy so-and-so. Sometimes you hear a piece that's so good you could die. It's just such an incredible thing to be a classical musician."

But it's not everything. Her tastes in listening, if not in performing, include a lot of other styles: "I like Ella; Elvis, not because his music is great but he is intense; Barbra Streisand--I learned a lot about phrasing from Barbra Streisand; the Beatles, when I'm in the mood, and I'm into Dixieland now, since I went to New Orleans. A lot of young musicians come to Juilliard; they're in possibly the greatest town in the United States as far as performing arts are concerned. They don't go to the ballet. It's right there, you don't even have to cross the street: two of the greatest ballet companies in they world. They don't go to the opera--it's right there. They don't go to see Broadway shows; they don't go to the museums; they don't go downtown to listen to jazz in the Village. They sit in the practice rooms. It's sad. That's very important to be really well-rounded."

Whether or not she is well-rounded, her life has many angles. She is constantly busy with things that are none of a young musician's business: ceramics, softball, sanding machines and cooking utensils. She has just bought a wok and is learning the mysteries of Chinese cooking. She is making a ceramic chess set for a friend who wants to learn the game. She has just finished a massive two-week project of renovating her aged apartment far uptown on 102nd Street.

"I did everything myself," she says proudly. "I almost lost my hands--cracked and all kinds of polyurethane on them, it was terrible. I thought it would take two days, but it took two weeks. If you start plastering, the whole wall falls off, so I had to scrape the whole wall, plaster the whole wall, then do a double coat of paint, sanded the floors, sanded the walls, changed the linoleum. It was hard work, but it was great fun and the whole place is completely renovated. It cost under $200 for plaster, paint and everything."

Nadja Salerno-Sonnenberg grew up poor, and at the beginning of a career that should make her very wealthy, she still counts pennies. "I really need air-conditioning," she muses. "This is the first summer I have spent in Manhattan. Usually, I would be at Aspen or somewhere, but this year I'm too busy. It's hard for me seriously to get up and start practicing in my apartment, and with the heat and the humidity, it's no good for the violin."

Next year, she is scheduled to give 40 or 50 concerts. Meanwhile, she is still coming to terms with the fact that she is no longer a Juilliard student. She is a star being born, and not without birth pangs.

As for the violin, it is the instrument that was given to her and the one that will dominate her life, but she considers herself more a musician than a violinist. "When I was very young," she says, "it was not the violin that excited me but music--orchestral music and opera, particularly opera. I think I could have been as good on the piano or the cello. The violin is simply what I use to make music."

And the music is what she uses to communicate, but she thinks that everything in her life goes into her performance--Italian sausages and softball, auto-racing and getting drunk. "How do you know what to say in the music," she asks, "if you spend all your time practicing instead of living?"

On one memorable occasion, her music and her life interacted with particular intensity. She had had a fight with "a very special person," otherwise unidentified, who she knew would be in the audience for a recital of hers. "I was going to play Gershwin's 'It Ain't Necessarily So' for my encore," she says, "but at the last minute I decided to switch to Rachmaninoff's 'Vocalise' and to put into it everything I had to say. It worked, and everything is fine now. Thank you, Mr. Rachmaninoff."

Throughout the interview, she spoke of other violinists without any trace of competitiveness except at one point when the name of Itzhak Perlman came up. He once made her jealous:

"I'm sitting at home watching the Yankees--it's a dull evening and I'm watching them lose. Suddenly, I hear this very familiar voice in the box, announcing it. I said, 'My God, that's Perlman, what the hell is he doing in the box?' He was the announcer for the Yankees for one inning and I would like to know how did he get up there? How did this classical violinist get up in the box? I mean, he was great, he was funny, and I have to say I enjoyed it immensely. You know, he lives in Babe Ruth's old apartment, but how did he get up there? Imagine all the people that are working for the Yankees and all the people that are involved in sports. How did he get up there? I want to do that.

"Of course, I'd really like to play for them, but I'm a girl--that's my handicap. But I think there's a goal that some day, if I really become famous, I could do it. That would be to play the national anthem at the World Series. That would be great. Only if the Yankees are in it, of course. I wouldn't do it for the Dodgers. Boy, that would be the biggest crowd I ever played for . . . and maybe throw the first ball out, too. If I did, it would reach all the way to the pitcher without hitting the ground."