The cast of the American Repertory Theater’s “The Glass Menagerie’’ — Brian J. Smith (left), Zachary Quinto (second from left), Cherry Jones (second from right), and Celia Keenan Bolger, — joined their director John Tiffany in New York on Tuesday to promote their Broadway run, which starts next month. Tiffany, of the musical “Once,’’ opened his production of the Tennessee Williams play in Cambridge in February. It was Broadway-bound by April.