His early career was spent performing in Off-Broadway productions, including Class Enemy in 1979, for which he won a Theater World Award for a stage debut. His first major Broadway credit was the ill-fated Stephen Sondheim/Hal Prince/George Furth musical Merrily We Roll Along (1981), which underwent constant changes during an unusually long preview period and closed after only sixteen performances. His next show, 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 - ran for eight months.

Price served as Associate Artistic Director for the American Jewish Theatre from the late 1980s through the mid-1990s. He was resident Director at Musical Theatre Works, a non-profit theatre dedicated solely to the development of new musicals until 2002, when he became resident Director.

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 in 1989 for the American Jewish Theater, followed by The Rothschilds and Juno, both of which received Outer Critics Circle nominations for Best Revival.

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.

In 2000, Price co-wrote (with Linda Kline), 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. The show was also nominated for four other Tony Awards, including Best Musical. He directed a Broadway revival of 110 in the Shade at the Roundabout Theatre Company in 2007, starring Audra McDonald. The play was nominated for the 2007 Tony Award, Best Revival of a Musicaal (among others).

In March 2010, he conceived and directed Sondheim: The Birthday Concert at Carnegie Hall, celebrating the composer-lyricist's 80th Birthday. The PBS television broadcast was nominated for several Emmy Awards, and Price won for 'Outstanding Directing For A Variety, Music Or Comedy Special'.

In April 2011 he directed an acclaimed concert production of Sondheim's Company with Neil Patrick Harris, Stephen Colbert, Martha Plimpton, Christina Hendricks, and Patti LuPone, backed by the New York Philharmonic.

Possibly his most significant Off-Broadway stage credit as an actor is the william Finn – James Lapine musical Falsettoland as Mendel in 1990.

In 2016, Price directed the documentary Best Worst Thing That Ever Could Have Happened, which chronicles the ill-fated journey of Stephen Sondheim and Harold Prince's original 1981 Broadway musical Merrily We Roll Along.