ISAAC STERN, leaning back into an easy chair at his Boston hotel suite, looks more like a middleaged, ruddy precinct pol than the man almost unanimously regarded as the most exceptional violinist now before the public.

A cigar is in his hand and the shirttails of his checked short-sleeved shirt are out. His horn-rimmed, bifocals are shoved back over his fading mane. Eight hours later he will enter the white-tie world of the Boston Symphony, tackling the Mendelssohn concerto for Lord knows how many times in a week.

But what is on his mind is, well, tennis.

It has been a pssion of his over the years -- on the court, in the stands and from the television screen. And sometimes combining his work and his tennis has caused problems. In recent months Stern has followed a strenuous concert schedule as he has moved from country to country performing three or four nights a week, all keyed to the celebration of his 60th birthday on July 21.The events continue with a series of five concerts beginning at the Kennedy Center tomorrow night.

But, he says gleefully, "We somehow managed to arrange things so that we were in Paris during the French Open, in London during Wimbledon and in New York for the U.S. Open. Occasionally we manage to get some perks in this business too, you know."

Among the other features of the international tour so far was a dinner in Stern's honor at the American Embassy in Paris that marked the first and only time that French President Giscard d'Estaing has graced that place with his presence.

But for all his international acclaim, Stern remains a quintessentially American artist, his love of tennis only one sympton.He was born in Russia, but his family moved to San Francisco long before he can remember, and that was his boyhood home. When it is suggested that he identifies inextricably with American values -- unlike so many musical stars today who cultivate a transatlantic identity -- Stern pauses for a minute.

"I never thought of it that way. That scares me. But in a way it's very right. I grew up here. I know it intimately. I know all kinds of life in this country, from the high points of things, like football, to the low points, like politics."

He puffs on his cigar, grins and there is laughter.

Even in the midst of an international celebration of his career, this man who numbers heads of state among his friends is very much at ease with the details of day-to-day life. As Vera Stern, his wife of 29 years, answers the jangling phone, Stern keeps impressing on her that she must get going on a drive to their country home in western Connecticut, in time to meet a decorator who is directing the renovations of parts of it recently damaged by fire.

He is rattling off telephone numbers for her ("I happen to have a terrific head for numbers") and advises her on the route ("Vera, I know Route 22 is longer but you will get there much faster").

Things eventually gathered together, she makes her departure. And Stern settles in to talk about the state of the arts. The Consummate Politician

Stern was not a conventional child prodigy, and it was probably a blessing. He was 8 before he took up the violin, and 14 before he played professionally. hA few years later he was concertizing feverishly and by 25 he made his first concerto recording. Since then he has been one of the most prodigious, and successful of classical recording artists.

In his years on the concert stage, though, Stern has become more than just a superlative musician. He has become a major cultural force -- at the federal, state, and local and international levels, or any other place his strong convictions may take him. He is music's consummate politician. The extracurricular high points were summarized quite simply a couple of weeks ago in this speech, which New York Philharmonic conductor Zubin Mehta delivered live on national television before a concert:

"Tonight, Isaac will simply play. He will not be leading a board meeting at Carnegie Hall, he will not be holding seminars on Israeli foreign policy, or be advising some other city on a new hall's acoustics or introducing to the public new talent that he has discovered."

Among his accomplishments, Stern:

Led the drive in 1960 to save Carnegie Hall from the wreckers' ball and now serves as its president. "We had to do most of that by long distance," he says;

Was a founder-member of the National Council on the Arts. "President Johnson, in his colorful way, said 'I don't know dash dash expletive-deleted about the arts but . . .'";

Is board chariman of the America-Israel Cultural Foundation and music adviser to the Jeruselam Music Center (there are few Israeli leaders he has not know well);

Is a clebrated crusader against most contemporary acoustical engineering "gimmickery";

Has been a mentor of such noted younger players as Pinchas Zukerman and Itzhak Perlman. "There is now a new generation of people coming along and we will peform with some of them at Carnegie Hall Nov. 1";

Even played the violin solo in John Williams' Oscar-winning soundtrack for "Fiddler on the Roof."

How in the world can the most famous of violinists function on so many levels at the same time, and how did he get there in the first place?

Pianist Eugene Istomin, his old friend and chamber-music partner, speculates: "It's the tremendous force of his presence. It comes from nature. Lots of people try for it, but few arrive at the goal. You know, Isaac is not a particularly handsome man -- not a prepossessing-looking person.

"But he has this tremendous capacity, and desire, to communicate with other people. And it has taken the form for a long time of a remarkable love affair between him and his audiences. With other musicians this desire is expressed exclusively in the playing, and some others are just plain show-offs." Around the Arts

Stern talks about national arts policy, something he was involved in long before most elected officials realized there was such a thing. He has had many successes -- because, among other things, he has the politician's knack for persuading people by talking to them on their own terms.

Asked about the early days of the National Arts Council, he says, "I was the one who talked to President Kennedy first about it. It was in a private meeting arranged by Pierre Salinger [Kennedy's press secretary]. And that was the last time I saw Kennedy on that subject. It was about a month before he was killed.

"But then Johnson came in, and Pierre stayed on. He was still interested in the field of grants and I remember seeing Mrs. Kennedy again at that time.

"Then I saw Abe Fortas, one of the men I knew very well -- he acted as a lawyer for me at a time. He was Johnson's closet adviser. And I talked to Abe about it and he arranged for me to work with Johnson.I went in to see him at the White House. And Johnson, in his colorful way, said, 'I don't know from dash dash expletive-deleted thing about the arts. But if it's important, this is the way it's going to be and I'm goin' to keep my cotton-pickin' hands off it. But I'll put it through.' And that's one of the things that started it.

"I remember we had a meeting in Tarrytown -- I think it was three days -- and there was Tony Bliss, Agnes de Mille, Leonard Berstein, Father Hartke, Greg Peck, George Stevens Sr. and at the first meeting we were sitting around and Lenny said, 'What are we about? What is our reason? . . . Finally we decided that the main thing was to do two things: One was to buttress and expand existing institutions of excellence and the other was to give individual artists the right to fail. And we took off from there.

"There was some talk about needing a chairman, and we talked it over and the name of Roger Stevens came up. And I was the one to call him. He accepted, and that's how that came about."

As to the present workings of the Arts Endowment and its council, Stern is a little queasy: "I think there is a little too much of a political nature right now in both councils. I would like to see it much more on the order of the Kennedy council, where a large sum of money is put aside and a professional group administers it -- a professional group that see the country as a whole."

Too much money, he says, "is in the office in Washington. The bounds of the bureaucracy that is growing around us in Washington is enormous. Why, when we were there we were just a handful -- the council, five or six heads of departments and half a dozen secretaries. That was it."

Turning to the subject of orchestras, Stern is troubled by the possible cancellation of the Metropolitan Opera season. But the most serious threat, he says, is "what might occur if -- in the enormity of attention-taking apparatus available today, through television, radio, concerts, sports -- they may find that people suddenly can get along without the Met. I don't think they can do without opera."

This subject reminds him of a recent and controversial article by conductor/composer Gunther Schuller decryng morale problems in many American orchestras, despite the fact that, as Stern says, "the whole standard of orchestral playing in this country has reached a level matched by only two or three other orchestras. The article is correct from beginning to end, except that it does not give specific remedies so far as the musicians are concerned. It just states the problems.

"I know it says that board members should be more educated, should go and know more about what's doing and raise enough money and involve themselves in artistic discussions. But that's not really what the problem is: He was talking about the orchestral musician guarding his enthusiasm. That is recurring everywhere because you cannot grind out music as you do automobiles, and I'm not sure how many hours a week even the best musicians can keep their burning enthusiasm. Today, sometimes they just play notes.

"I'm not sure what engenders it, whether it is the fact that standards have risen and the seasons have leghtened, or if it's that there are so many conductors who are not exactly the kind who strike fire every time they lift a baton." Picking Up the Guarneri

Midway through this wide-ranging conversation, an in-house phone rings and Stern talks for a moment with an apparent stranger in the lobby, telling him to come on up. "This is going to be difficult," Stern warns. "This is someone who has inherited a violin and probably is hoping against hope that it is valuable."

Presently an aging man appears at the door in rather tattered clothing, and opens a violin case to display a battered 20th-century instrument modeled somewhat after Stern's own Ysaye Guarneri, one of the world's most valuable violins. (it once belonged to the turn-of-the-century virtuoso Eugene Ysaye.) Stern begins with a gentle warning, "i warned you before that modern instruments are rarely very good."

But this violin has worse problems than that -- bad varnish, a bad bridge and bad sound posts. He gently repeats his judgement in several ways to the elderly man. "it's a serviceable instrument for a student but beyond that, there isn't much value in it by now. The art of great violin making died about 1800 and it hasn't been reborn yet. Nobody knows why."

Stern picks up the man's violin and does some exercise on it. Then, he takes the Yasay Guarneri from his case and shows the spectaculr difference.

Escorting the man to the door, he says, "I wish I had better news for you, but there's nothing else I could tell you."

Given his way with people and his interest in politics, Stern is asked if he ever contempled running for office. "No," he says, "it's not really right for me. I tend to be more an ideas sort of person. I'm more inclined to take a stand on something about which I feel very strongly than hammer out the details of an agreement. Sometimes I get impatient with the nitty-gritty."

In his travels has he ever quitely undertaken a diplomatic mission? "No. But I was very much involved in starting the cultural exchange with Russia. In fact, I was playing in Russia before there was an exchange program. That was 1956."

What, then, about his friendships in recent years with statesmen around the world -- from Henry Kissinger to the French president? After all, musicians are not limited to four-year terms.

"Any idea that any artist has any political clout is utterly wrong. The only value that he has is because of his notoriety. Remember that there are people in politics who love the arts. there was Prime Minister Menzies of Australia. He wasn't that involved in music, but he loved poetry. And, of course, Ted Heath loves music very much and he's a pretty good conductor. Hubert Humphrey loved people in general, he admired artists enormously and he loved this country more than I think any American I have ever met." Off the Circuit

For all the physical toil of this year, Stern does not talk like a genuine workaholic. During the first 9 1/2 months of next year, Stern has held his concert schedule back to eight weeks.

"Everybody says, 'What are you gonna do? What are you gonna do?' But I said, 'That's the point of a rest: I don't know what I'm gonna do.' First of all, I have to sleep for two or three weeks, because it takes me that long to slow down.

"And then I'd like to read a lot and I'd like to play some music that I haven't really taken apart and thought about for a long time -- lots of new music. Concerts to go to. Operas. Plays, and I would like to get up in the morning and just do whatever I feel like that morning. If it's to play a little Bach, okay. If it's to take a walk and look at an antique shop, go ahead and walk. I haven't done that in 35 years.

"Our house in the country is not near the water. Not near the cocktail circuit. It's just quite and comfortable, a lovely place."