I go to NYC several times a year, often going with fast and cheap restaurants in mind (I'm too lazy and type-B for out of control). Here are a few suggestions:
-- Cascina (Hell's Kitchen): A charming Northern Italian dining spot with excellent food and decent prices.
-- La Caridad 78 Restaurant (Upper West Side): A Chinese/Cuban restaurant with really surly waiters but good food.
-- Trinity Place (Lower Manhattan): A quiet, low-key restaurant located in an old bank vault.
-- Bubby's (Tribeca): A local favorite, with tasty comfort food dishes and some truly amazing pies.
-- Veselka (East Village): Excellent Ukrainian food in a typically bustling New York dining spot.
-- Moran's (Lower Manhattan): A quiet and friendly Irish pub located in an old church on a narrow side street near the WTC site.
-- Arturo's (Greenwich Village): An often overlooked, old-school pizza joint with lots of character.
-- Moustache (West Village): Good Middle Eastern food on charming Bedford Street.
-- Diamond Dairy of New York Restaurant (Diamond District): A truly unusual Kosher place upstairs/in the back of a jewelry store.
-- Topaz (Midtown): An excellent Thai restaurant that isn't very well known because it's on one of the quieter streets in Midtown.
There are others I've been to, but I can't think of them right now! Perhaps I'll post more later...