Birdland -- there is usually a late jazz show at 11 and the kitchen is open til 1 AM. It's at 315 W 44th Street. The food is very good, as is the service, and the jazz is always first rate.
Although you didn't ask -- on Fridays starting around 5:15 there is an hour-long big band jazz show made up mostly of Bway pit players who love big band jazz (they can fit 16 players onstage). So it would be pre-theater, have dinner, hear a bunch of great musicians from various Bway pits -- and maybe one might be from the show you are about to see. Everyone I have ever recommended this to as pre-theater on Fridays has RAVED!