Forgive me if this has been mentioned here before but, if it has, I don't recall seeing it...
Although there are now several really inexpensive dumpling stands in Chinatown, I just found perhaps the most conveniently located one (if you're coming from the West), in perhaps the most incongruous place of all: as a standalone cooking station inside the seating area of the "Popeye's Chicken & Biscuits" on the Bowery, just north of Canal.
We popped in there by happenstance yesterday and tried two different kinds: a steamed pork soup dumpling and a boiled pork & chives dumpling.
Although both were rather doughy (i.e. rather "potstickerish") compared to what's found at a more expensive sit-down restaurant, the fillings were surprisingly tasty, especially when combined with the vinegar dipping sauce. And, at 10 dumplings for $2, I'd wager to say it's the best food deal anywhere in Manhattan!