The nation's first 1-person improv jam (now spread to Denver and KC) is at Backline every 3rd Thursday at 10pm (this month is special and at 11pm.) Anyone can get up on stage if they wish to, and each person gets 1-3 minutes to improvise anything they want to.
Maybe an improvised TED Talk, or poetry slam? How about an excerpt from an audio book, public confession, sermon, or even 1 improviser being multiple characters in one scene.
It can be terrifying to perform but usually awesome to watch. Also, show up early for 3 great hours of improv from 8-11pm!