Chat and Chew, just off the square on E. 16th street is dependable and in your price range. http://nymag.com/listings/restaurant/... Give them a call first, however, someone mentioned they might be closed for renovations.
Small correction: It was Zen Palate. If the food was as horrible as what is served at their flagship location on 9th Av., then I think it's no great loss. Can't say anything about Fatty Crab since I've never been.