* THE FIRST NEW YORK INTERNATIONAL FESTIVAL wound up its program of 350 events on July 11, with a free concert by Placido Domingo in Central Park, and fireworks. Chairman Martin E. Segal estimated that the 31-day affair had brought $400 million in business to the city, with performers from 31 nations and more than 100 world premieres. American Express was the founding sponsor, contributing $3 million of the $8.5 million cost.

Some of the outstanding festival performances were given by the Maly Theater Company from Leningrad; the Dance Theater of Harlem; the Paris Opera Ballet; American Ballet Theater; Frankfurt Ballet from Germany; Pierre Boulez Ensemble from Paris; the Chicago, Montreal and St. Louis symphony orchestras; the London Sinfonietta; JVC Jazz Festival; Dublin's Gate Theater; and the Yale Repertory Theater, which presented two Eugene O'Neill plays on Broadway as a salute to the playwright's 100th anniversary.* IN LENOX, MASS., the Boston Symphony Orchestra looks forward to celebrating Leonard Bernstein's 70th birthday with a gala performance at the Tanglewood Festival on Aug. 25. Beverly Sills will host many friends and colleagues, such as Lauren Bacall, Hildegard Behrens, Victor Borge, Van Cliburn, Gwyneth Jones, Yo-Yo Ma, Roddy McDowall, Midori, Mstislav Rostropovich and Frederica von Stade, in guest performance.

The gala will launch a four-day celebration that will include performances by the Boston Pops Orchestra and Tanglewood Festival Chorus. Conductors John Williams and Seiji Ozawa will be joined by John Mauceri and Michael Tilson Thomas, two of the many outstanding conductors whose careers Bernstein has guided. Bernstein requests that proceeds from the gala go toward ensuring the continuation of the Tanglewood Music Center, a place of special significance for him for almost 50 years.

* THREE MAJOR BROADWAY FIRMS have sued New York City and its Landmarks Preservation Commission over the issue of landmark designation.

The suit - filed by the Shubert, Nederlander and Jujamcyn organizations, which control 22 landmark theaters - contends that "landmarking entails restrictions which are unfairly costly and prevent the theaters from accommodating current stage technology," according to Variety.

The suit also alleges that various zoning and demolition requirements applied to landmark theaters prevent owners from fully exploiting their houses and "sharing in the economic growth of the west side of midtown, with the greater part of the value of their properties taken from them."

The city of New York has 30 days to respond to the suit, which may have far-reaching ramifications.

* DANCER RUDOLF NUREYEV celebrated his 50th birthday on stage in New York recently, in a gala performance by his Paris Opera Ballet, with a galaxy of international stars, including legendary partner Margot Fonteyn, joining him on stage. Still dancing, Nureyev received an ovation for his Wanderer in Maurice Bejart's "Song of the Wayfarer." In the past four years, Nureyev's artistic direction has revitalized the Paris Opera Ballet.

* DANCER MIKHAIL BARYSHNIKOV is sidelined for the summer with a knee injury that requires surgery. He had planned to open a national tour on July 1, but was forced to cancel. He has also canceled several festival appearances in Europe.

* THE COLON THEATER in Buenos Aires, once a foremost opera house that attracted international stars, has fallen upon hard times along with Argentina's economy. For the first time in 80 years, all opera performances at the Colon were cancelled for the 1988 May-December season so new mechanical stage equipment, including a computerized control system and new elevators, could be installed.

Two symphony orchestras will perform at the Colon, but Argentines, half of whom are descended from Italian immigrants, will miss their opera. Colon general manager Ricardo Szwarcer says that when the opera re-opens in 1989, it will have humbler goals, with few international stars.