UCBT is the best place for comedy in the city hands down. and at 5 dollars a show there's no reason not to go. You'll see many familiar faces from SNL as well as the young up and coming comedians. Definitely a "Thing to do" in the city.
My favorite spot for comedy in the city with lots of free shows (like Asssscat 3000 Sundays @ 7:30PM). Also offers classes on longform improv, sketch writing, and various other comedy skills. This place does not disappoint.