Going, the oldest of six children, was born in 1963 in Washington, D.C. to the late John Burke Going and Lorraine M. (a police dispatcher). She was raised in Newport, Rhode Island and graduated from Rogers High School in 1981. Going then attended Emerson College for two years, before studying at the American Academy of Dramatic Arts.
Going has dated musician Adam Duritz and screenwriter Harley Peyton. She married actor Dylan Walsh on October 10, 2004. The couple have a daughter, Stella Haven Walsh (born November 22, 2003).