I have to agree with ChinaTown. You get some really great stuff there if you know where to look.
But so long as you stay away from the Chains in Times Square, or the High Brow places (steak houses that charge $10 for creamed spinach??? CREAMED SPINACH??!?) you can find MANY places that serve some great foods.
Right now the easiest seem to be various asian foods (I think Korean Alley has some great soup/tofu/stew places that are pretty inexpensive.... until you order the Seafood Scallion Pancake!!
), Indian foods, especially in the carts, and some other "ethnic" variants.
There are also the Lunch Specials at some places allowing a decent meal for $10 or so.
The hardest to find IN the city are GENUINE mexican (not Caliente Cab, NOT Chexican, and not Burritoville/Blockhead/Chipoltle), "old school" family Italian (that you do not have to pay over $12 for a plate of ziti with tomato sauce on it), GERMAN (my god, amazing how many cuisines can't make a decent Wurst!). You can find some strange small spots, but I am still amazed we do not have things like Crepe shacks (saw them on vacation, just get one made and handed over in font of you like it was no more than a hot dog!).
All said though, I am so spoiled on NYC. There are some otehr cities that do compare, but looking at neighborhoods in the burbs.......
Well, lets put it this way. I am reminded of my own Mayonaise roots.