Goetz made his Broadway debut as John Barrymore in the 1981 Colleen Dewhurst-directed play Ned and Jack, which closed on opening night. Additional New York City theatre credits include Beyond Therapy, Brighton Beach Memoirs, The Government Inspector, The Last Night of Ballyhoo, Macbeth, and the off-Broadway productions The Jail Diary of Albie Sachs and Alan Ayckbourn's Comic Potential.