Alice Tully Hall at Lincoln Center is one of the most famous performing spaces in New York City, and the woman behind it was one of the city's most private philanthropists. This intimate memoir is an engaging encounter with a gracious and influential supporter of the arts.     Albert Fuller's close friendship with Miss Tully over a period of more than thirty years allows him unique insight into her eventful life and colorful personality. The daughter of a Corning heiress and a state senator, Miss Tully trained as a singer in Europe before turning her love of music toward enlightened philanthropy. Chair of the board of directors for the Chamber Music Society of Lincoln Center for nearly twenty-five years, she also served on the boards of the Metropolitan Opera, the New York Philharmonic, and The Juilliard School, and as a trustee of the Metropolitan Museum of Art, the Pierpont Morgan Library, and the Museum of Modern Art. For her cultural contributions, New York City awarded her the Handel Medallion, and France conferred on her the three steps of the National Order of Merit as well as the prestigious Legion of Honor.   A charming woman whose activities influenced the musical tastes of New York City and the nation, Alice Tully reveals herself here for the first time.    Through this privileged portrait we discover an individual whose public generosity was matched by private courage, a quick intelligence, unfailing social grace, and a fierce and fearless love for life.