Born in New York City, Price grew up in Metuchen, New Jersey. He attended the Fiorello H. LaGuardia High School of Performing Arts. His early career was spent performing in off-Broadway productions. His first major Broadway credit was the ill-fated Stephen Sondheim musical Merrily We Roll Along (1981), which underwent constant changes during an unusually long preview period and closed after only sixteen performances. He had better luck with his next project - the Athol Fugard play MASTER HAROLD...and the Boys, in which he portrayed a South African student opposite Danny Glover and Zakes Mokae as the family servants - which ran for eight months.

Price made his directorial debut with the off-Broadway revival of The Education of H* Y* M* A* N K* A* P* L* A* N, followed by The Rothschilds and Juno, both of which received Outer Critics Circle nominations for Best Revival. His most significant off-Broadway performing credit is the William Finn – James Lapine musical Falsettoland.

Price's work with the New York Philharmonic includes:

In 2000, Price co-wrote, directed, and starred in A Class Act, based on the life and career of composer – lyricist Edward Kleban, whose sole Broadway credit was A Chorus Line. The score consisted of songs Kleban had written for other shows that remained unproduced. After a two month run at the Manhattan Theatre Club, it transferred to the Ambassador Theatre, where it fared less successfully and closed after three months. It earned Price his sole Tony Award nomination to date, for Best Book of a Musical.

Price served as Associate Artistic Director for the American Jewish Theatre from the late 1980s through the mid-1990s. He currently is resident director at Musical Theatre Works, the only non-profit theatre dedicated solely to the development of new musicals. One of his latest projects was a Broadway revival of 110 in the Shade, which opened in May 2007 and ran for 94 performances.

Price's limited film and television credits include small roles in The Muppets Take Manhattan and Dirty Dancing and guest appearances on The Golden Girls and Law & Order. Behind the scenes, he was a staff director for the ABC soap opera One Life to Live, for which he was part of a team that received a Daytime Emmy Award nomination for Outstanding Drama Series Directing in 1995.