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The restaurant to the farthest north (by the NY public library) is the
Szechuan Gourmet on 21 West 39 Street. This will probably be a miss, but a just in case spot. It gets mixed reviews from chowhound, but it is cheap and within walking distance. The next one, headed south, Woorijip on 12 West 32nd Street. Here is one of the big reviews:
This place is so great... I come here every other day! All the food is cooked fresh every day. There is a wide array of hot and cold dishes and snacks all ready to go in take-home containers. During lunch & dinner, they also have a delicious Korean buffet for only $6.49/lb. Best of all, the place is open from 6am-3am, so you can grab delicious fast food at almost any time of day!! Be sure to try the grilled eel lunch box... So tasty and only $5!
Nearby the hotel and the cooking school is Rickshaw Dumpling Bar on 61 West 23rd Street. They have very inexpensive, pretty good food.
There is Wichcraft on 11 East 20th Street. Their menu looks great for lunch, and word has it that the dinner menu is not expensive, either. I will be nearby book shopping.
I have left off two restaurants that might make the cut, Nisos and Lucky's Famous burgers.