If you follow the NY foodie blogs or Bourdain's TV show, this is old news. For the rest of you, check it!
Xi'an Famous Foods is cheap as hell, and serves some amazing food. Liang Pi is the dish you cannot pass up: thick, springy noodles like nothing I've ever had, with spongy wheat gluten pieces to soak up the yummy, spicy sauce. Four bucks gets you a huge plate that will fill a total pig, or a rickshaw driver. The cumin lamb burger is great too. Tiger Vegetable Salad should be called Dragon Breath Salad, which is cool if yer into that.
The new East Village location is more convenient for the average visitor, but nothing beats the filthy rabbit warren that is the Golden Shopping Mall basement in Flushing, Queens.