Nixon was born in New York City, New York, the daughter of Anne Knoll, an actress, and Walter Nixon, a radio journalist. Her first onscreen appearance was as an imposter on To Tell the Truth, where her mother worked. She began acting at age 12 as the object of a wealthy schoolmate's crush in The Seven Wishes of a Rich Kid, a 1979 ABC Afterschool Special. She made her feature debut co-starring with Kristy McNichol and Tatum O'Neal in Little Darlings (1980). She made her Broadway debut as the bratty Dinah Lord in a 1980 revival of The Philadelphia Story. Alternating between film, TV and stage she did projects like the 1982 ABC-movie My Body, My Child, the features Prince of the City (1981) and I Am the Cheese (1983) and the 1982 off-Broadway productions of John Guare's Lydie Breeze. In 1985 she appeared alongside Jeff Daniels in Lanford Wilson's Lemon Sky at Second Stage Theatre.

Nixon graduated from Hunter College High School, and made theatrical history while a freshman at Bar