Stanley was a successful Broadway actress with only a few film roles. She was singled out by The New York Times critic Brooks Atkinson for her early work. She eventually attended the Actors Studio, studying under Elia Kazan, Lee Strasberg, and Vivian Nathan. She received the 1952 Theatre World Award for her performance as Anna Reeves in The Chase,Internet Broadway Database: The Chase Production Credits and starred in such Broadway hits as Picnic (1953), playing Millie Owens and Bus Stop (1955), playing Cherie.
