Came up with a few recs as I live in the area. Mostof these places are open until at least 10pm, some til 11pm:
-Bon Bon Chicken (Korean fried chicken) on Chambers bet B'way and Church. Good stuff, get the sweet and spicy combo. I don't think they have the slaw anymore and the service can be a a bit slow. If getting takeout, call ahead.
-Carl's Steaks (cheesesteaks) on Chambers about 1/2 block closer to B'way (not crazy about them but have had a good cheesesteak there before). Skip the fries.
-Sophie's Cuban Cuisine(really good pernil with beans and maduros)-this is the only place that may close before 7pm. May be cash only.
-Gee Whiz Diner (corner of Greenwich and Chambers)not crazy about it, but my girlfriend's family loves it. Standard Greek diner, a bit pricey, although probably just standard NYC diner prices.
-The Soda Shop (Chambers bet Church and West B'way) good breakfasts and sweets, but haven't had dinner there yet, dinner menu looks good though.
-Kitchenette (Chambers bet. West B'way and Greenwich) good comfort food, a bit pricey, but I like it a lot. Good mac-n-cheese, turkey meatloaf, turkey club sandwich, roasted garlic fries, tasty baked goods too (cupcakes, cobblers, bars).
-Il Mattone (Greenwich bet. Hubert and Laight), Italian good grilled chicken sandwich w/mozzarella and roasted peppers, decent chicken parm. Never been there, always had delivery.
-Bubby's (Hudson @ N. Moore) comfort food, great pie. Haven't been to this one in years as it can be crowded, usually go to the DUMBO locale.
-Across B'way-Les Halles (John St near B'way) French brasserie-mussels, steak frites, french onion soup, macaroni and cheese, good burger. One of my favorites, not sure if they do takeout.
-Zaitzeff (corner of John and Nassau) really excellent burger and fries combo of regular and sweet potato fries. Never been there, always had delivery.
-L&L Hawaiian BBQ (Fulton St near Gold) I'm not crazy about it, but I have friends who swear by it.
Most of these are listed on menupages.com and I've ordered delivery for Kitchenette, Il Mattone and Zaitzeff on seamlessweb.com. Hope this helps.
These are more lunch places than dinner places. Second Zaitzeff. Zaitzeff has the BEST sweet potato fries, it's a small place (dining in was better before they switched to plastic silverware and paper cups!). I respectfully disagree with billyboy and cannot recommend Les Halles. L&L is practically fast food. OP what's your price range? What are you looking for (cuisine, atmosphere)?
You are a short walk from Seaport area (limited choices, a few good ones) and TriBeCa (better dining). You might want to do a search of this site there are many threads. I like Duane Park Cafe (prix fixe dinner $35) in TriBeCa and Acqua near the Seaport. Duane Park Cafe will be closing in January for renovations.