Born in Seattle, Damon was raised in Tacoma and graduated from Stadium High School, moved to New York City at age 16 to pursue ballet and ultimately appeared in several Broadway productions, including Shinbone Alley, Foxy, Flora, The Red Menace, The Boys from Syracuse, The Last of the Red Hot Lovers, Sweet Bird of Youth and The Cherry Orchard. During the 1967-68 season, she was the Mame and Vera understudy for the Angela Lansbury-led tour of Mame.