The Roger L. Stevens Center is the primary performance venue downtown, a beautifully restored 1929 movie palace with a baroque-revival interior. Owned and operated by the University of North Carolina School of the Arts, it hosts the school's professional-level student productions — opera, ballet, drama, film — along with touring shows. The students are good enough that this is genuinely worth checking the calendar before you visit the city.
The exterior, a triple-arched Spanish-Italianate facade on Fourth Street, is a downtown landmark. Even if you don't catch a show, walk past after dark when the marquee is lit.