There is a cheap tasty Japanese noodle bar Men Kui Tei on 56th just east of 6th Ave. I keep experimenting with what I order and I keep finding new things I love. It has enthusiastic competition which I have remained on the sidelines of, but you could search.
In the course of your month, if you wind up looking for late night food, Park Blue on W 58th between 6th and 7th (across from the Jumerieh Essex Hotel) is worth a try. Small menu of small plates, French/Mediterranean food. Good winelist though oddly all 1/2 bottles; good cocktails.
Also serving late night, a bit farther west, Landmarc at Columbus Circle. Menu can be hit or miss, but generally the beef is good, pork is good, the salads are good, oysters, mussels and sides are good. Can't recommend you depart from those. large good wine list is attractively priced.
For spicy chinese you are in the heart of it, but I prefer both Grand Sichuan (2nd Ave at 55th) or Szechuan Gourmet (39th between 5th and 6th) to Wu Liang Ye (which I also like)
Burger Joint (between 56th and 57th between 5th and 6th) a very casual burger and fries place hidden in the lobby of the Parker Meridien Hotel.
118 W 57th St, New York, NY 10019
21 W 39th St, New York, NY 10018
1049 2nd Ave, New York, NY 10022
10 Columbus Circle, New York, NY 10019
Men Kui Tei
60 W 56th St, New York, NY 10019
158 W 58th St, New York, NY 10019
DB bistro moderne is great. other thoughts would be the Bar Room at the Modern--can do small plates, or order off menu, don't need a reservation and they have great drinks. Also, a bit of walk but Artisanal on 32nd and Park ave if you don't mind walking. Their focus is cheese, and even have cheese sommeliers (?) to advise but its a biggish french bistro. Sushi: sushi yasuda is fantastic (42nd between 2/3rd) sit at the sushi bar and let the chefs do their thing. The Brasserie is an old standby on 53rd between park and lex--modern interior, range of food and prices..Also, Alfreddo on 49th between 5th/6th has some good pasta options...
Three famous chefs have casual French restaurants in that general vicinity.
dbBistro Moderne, on 44th, b/t 5th & 6th, is 4-star chef Daniel Boulud's take on contemporary French bistro cuisine. We've been there several times, the last being a couple of weeks ago for lunch, and needless to say, the food is delicious.
Benoit, on 55th, b/t 5th & 6th, is Alain Ducasse's French bistro. We had a very good dinner there, albeit quite a while ago. He has since brought in a new chef. Though I have not hear much about how things are now, I would certainly be willing to go again.
Gordon Ramsay's Maze at the London, on 54th, b/t 6th & 7th, serves superb French cuisine.
Stepping away from French, if you like Szechuan cuisine, Wu Liang Ye, on 48th, b/t 5th & 6th, serves some of the best. Menu on menupages.com
At the excellent Scandanvian restaurant Aquavit, on 55th, b/t Madison & Park, the Cafe is the more casual, less expensive dining room.