For David Lloyd Kreeger, president of the boards of the Corcoran Gallery of Art and the Washington Opera, philanthropist and amateur musician, summer is a standing invitation to fly across the Atlantic with his wife, Carmen.

"Our summer vacations are usually taken in Europe . . . usually in Paris. We combine our vacation there with meetings of the Atlantic Institute," says Kreeger, who serves on the institute's board of governors. This month the couple will again go to Paris, "not only to attend meetings but also for the opening of "Cosi fan tutte" at the Theatre du Champs-Elysees, a joint production of the Washington Opera and the Orchestre de Paris.

The Kreegers also go to Florence, Rome and Venice, "our favorites in Italy," and from time to time visit Switzerland, Belgium or Austria, along with Scandinavia, and Russia. Other favorites abroad:

* London. "Where we see friends and attend the theater."

South Africa. "Great physical beauty but also great unsolved social problems."

Although he and his wife have also enjoyed warm-weather vacations in the American West, one U.S. destination is their special "favorite winter resort":

* Caneel Bay. "It's on St. John, which is the smallest of the American Virgin Islands. The month of February . . . is the best time of year for Caneel and probably the worst time of the year for Washington. So every February for the last 24 years we have gone there." He describes it as quiet, very beautiful, with almost perfect weather. They swim "in an almost surf-less bay just as smooth as a swimming pool with water so clear you can see the sandy bottom even when 10 to 12 feet deep."

"People go for the complete privacy," Kreeger says with a hint of anticipation in his voice. "It's the best of all worlds."