There is a hotel very close to Bowery Ballroom called the Pioneer Hotel. Despite it's cheapness and closeness to the venue where the shows will be,
DO NOT BE TEMPTED TO STAY THERE. Unless you like tiny rooms with blood on the walls, of course.
The other places I've stayed in NYC have been nearer the Empire State, which may not be the right sort of location for your needs, but if you think that sort of area would be suitable for you, the
Herald Square Hotel was reasonably priced, comfortable, and clean.
I've also read good things about the
Washington Square Hotel, and that's probably in a more suitable location. (Actually, I'm thinking of going to NY for my 40th birthday next year, and Washington Square Hotel is looking like a good candidate for where I'll stay)