The word used is 寄席, which is sort of a broad term for "any sort of more-or-less old-fashioned entertainment hall where comic performances are given" - I didn't think "comedy club" would fit, and it's broader than just "a place where rakugo is performed". Obviously there's no perfect direct translation, it being a firmly culturally-situated thing. shrug
Hah! I think using Vaudville is a good way to put it- especially since Vaudeville included monolouge type performances. Nothing like someone who just wants to hear your performance~