The best Chinese depends on what regional type of food you like. IMHO, the best Sichuan (and Hunan--just ask them) restaurant in Manhattan is Sichuan Gourmet, @39th and 5th, but Wu Liang Ye (@48th) is decent, too. The best Shanghai and Cantonese restaurants in Manhattan are all in Chinatown; there are also a few decent Fujanese places along Bowery, but somehow most folks don't appreciate the Fujan cuisine at all.
The best Southern Indian food, IMHO, can be found between 23rd and 28th and Lex. (The 6th St is a tourist trap and I wouldn't recommend it at all.) I am not aware any good North-Indian/Punjabi place in Manhattan at all: your best bet is to take the 7 train from Grand Central to 73rd/Jackson Heights (ditto for Taiwanese and Thai food). If you must stay in the city, both Bukhara Grill @49th and Sapphire@CentralParkWest are considered decent, but I haven't been there for at least 5 yrs.
Italian: Sister restaurants Convivio and Alto
American: Steakhouse = Keens; BBQ = Daisy May's
Contemporary American: per se, Gramercy Tavern
French: Eleven Madison Park, Veritas, Jean Georges, Fleur de Sel, Allegretti, Picholine, Cafe Boulud, Tocqueville
Do you know what part of town you'll be staying in? Here are some of my favorites:
Chinese: Chinatown Brasserie, Wu Liang Ye
Indian: Bukhara Grill, Chola
Thai: Highline, Kittichai
French: Brasserie fare at Les Halles (Park Ave)
American: Peter Luger Steakhouse, Nougatine (New American)