I only know Chinatown, so here are my favorites.
New Green Bo -- Bayard St. They have great crab and pork dumplings, better than Joe's Shanghai IMO. Scallion pancakes are really good there too.
Joe's Shanghai -- Pell St. Same food as New Green Bo, very crowded most of the time, you'll have to share a table.
Big Wong -- Mott St. Good for a quick meal/snack. Food is very cheap, stick with the noodle soups, congee, or items served over rice. Stay away from their roast duck, it aint very good.
Ba Ba Malaysian -- Bayard St. Pretty good Malaysian food, tons better than the Singapore Cafe on Mott St. I like the Taro chicken, char kway teow, satay.
I also like the Taipan Bakery on Canal St. Lots of great pastries to bring home. When I go to Chinatown I usually eat at New Green Bo or Joe's Shanghai, just cause I love the food there.
--Ben