After winning an OBIE for his direction of "Spunk" (1989-90), which he had adapted from three stories by Zora Neale Hurston, Wolfe earned his first Tony nominations for the book and direction of "Jelly's Last Jam" (1992), a musical about the life of jazz musician Jelly Roll Morton. He then became the first black director of a Broadway production that was not black-themed when he helmed Tony Kushner's Pulitzer Prize-winning drama about politics, AIDS and religion "Angels in America: Millennium Approaches", winning the 1993 Tony as Director of a Play. He picked up another Tony nomination the following year for staging the second part of Kushner's epic, "Angels in America: Perestroika", and garnered two more Tony nods in 1996 for helming "The Tempest", starring Patrick Stewart, and the Savion Glover dance musical "Bring in 'Da Noise, Bring in 'Da Funk", winning for the latter. The magic ran out with his 1998 revival of "On the Town" when his controversial decision to replace Jerome Robbins' signature choreography came back to haunt him, and though critical response was slightly better for "The Wild Party" (2000), which he directed and co-scripted, it paled in comparison to his triumphs in the 90s.
Wolfe became one of the Public's three resident directors in 1990 and replaced Papp's hand-picked successor JoAnne Akalaitis after her troubled 20-month tenure in 1993, becoming the only person besides Papp in the theater's history to hold the title of producer. In the first five years after taking over the theater's reins, he saw its endowments quadruple from $10 million to $40 million. Though criticized in some circles for championing his own projects more than the other works at the Public, Wolfe proved an able administrator, returning the institution to the black by 1995 after seven years of operating at a deficit. As producer, his decision to move "The Tempest" to Broadway for a limited run netted a modest $325,000, while moving "Bring in 'Da Noise, Bring in 'Da Funk" to Broadway and the unprecedented decision to promote the show's national tour as well amounted to a huge windfall for America's most influential and powerful not-for-profit theater.