In 1973, Williams attained a full scholarship to the Juilliard School in New York City. He was one of 20 students accepted into the freshman class, and one of two students to be accepted by John Houseman into the Advanced Program—the other was Christopher Reeve. Per a New York Times article, "Williams left Juilliard during his junior year in 1976 at the suggestion of Houseman, who said there was nothing more Juilliard could teach him. Gerald Freedman, another of his teachers at Juilliard, notes that Williams was a "genius" and that the school's conservative and classical style of training did not suit him. No one was surprised that he left.
Williams maintained strong ties with Juilliard. In 1988, while he was starring in a New York production of Waiting for Godot, he made a surprise appearance and spoke with drama students. Three years later he received his honorary degree and this award.