ETA: I've added a few more places to the end of this post.
Places To Eat: If your looking to check out some culinary neighborhoods after a hard day of BEAing, there are several options.
Little India is located on East 6th St, between 1st and 2nd avenue, so called because just about the entire street is filled with affordably priced Indian restaurants. (Urban legend says that the restaurants all share one giant kitchen in the back.) You can also check out the East Village while you are down there. Make sure to stroll down St. Marks Place.
Or try Chinatown, also a fun neighborhood. I can recommendJoe's Shanghai. They don't take reservations so you may have to wait but turnover is quick so it shouldn't be too long. Don't expect to have a private table. Depending on your party size and what's available, your party of four may end up at a table for 8 alongside four strangers. But that's part of the fun. The soup dumplings are a must have. If you are in the mood for dim sum, tryOriental Garden Seafood.
If your staying in midtown, you might want to check out restaurant row. Located on W46th Street between 8th & 9th Avenues, in the heart of the theatre district, there are numerous options to choose from. My mother-in-law's favorite is Lidia Bastianich's Becco. They have a deal where you can choose an appetizer or salad plus unlimited servings of three daily pasta preparations for $22.95. If you go around 8pm, you shouldn't have a problem getting a table as the majority of their business comes from the pre and post theater crowds. I can also recommend Joe Allen's,a theatre institution. (There's even several scenes set in the restaurant in the musicalApplause.) The walls are covered with show posters - all from shows that have flopped. They're fun to check out. Another good place isAngus MacIndoe, a popular theatre hangout with pretty good food. If you are with a group, Carmine'sis the place to go. The Italian fare is served family style on large platters for the table to share. Also in midtown, Koreatown is located on West 32nd St between 5th & 6th Avenue. I can't recommend any specific places but, Hey, you're in NYC, be adventurous. See what looks good to you.
Other Places to Eat: Telepan - this is my favorite restaurant in NYC. It's not cheap but totally worth the price. Most ingredients are locally sourced and the food is fresh and delicious. The smoked trout appetizer is friggin incredible. Shake Shack - numerous locations around the city. There is one on W77th St & Columbus right across from the Museum of Natural History, if you happen up that way. Another is at 8th Avenue and W44th St. Schnipper's Quality Kitchen at W41 St & 8th Avenue, across from the Port Authority. I find it a bit pricey for what it is but the food is tasty and comforting. The Grand Central Oyster Barlocated in Grand Central Station. An institution. Amy's Bread- 672 9th Ave (btw 46th & 47th St) One of the best bakeries in the city and opened until 11pm if you get the late night munchies. 'wichcraft- bryant park11 west 40th street @ 6th avenue.Tom Colicchio's sandwich place. Sandwich Planet - 522 9th Ave @ 39th St. John's Pizza- 260 W44th St (btw Bdwy & 8th Ave). Whole pies only, no slices. Peter's Rotisserie - 587 9th Ave (btw 42nd & 43rd St) Home cooking style at a good value. I've had many a satisfying meal there and the folks are real nice. Keste - 271 Bleeker St (btw Cornelia & Jones St) If you find yourself down in the West Village, check out Keste. Terrific Napoli style pies.
Touristy but Fun: Ruby Foos - 1626 Broadway @ 49th St. Ellen's Stardust Diner - 1650 Broadway @ 51 St. It's a retro 1950s diner and the wait staff sings and dances. Carnegie Deli - 854 7th Ave @ 55th St. You couldn't pay me to eat one of these behemoths but I'm in the minority. Most tourists love it.
One final note: For god's sake, don't go to Applebees or Red Lobster! You'll be in New York City! Why go to a place you can go to in any mall around the country... But if what you really want is that chain experience, try a place like Junior's. At least you'll be in a place that first started in NY (well, Brooklyn).
If I think of any other restaurants, I'll add them to the end of this post but I think this list is a good place to start.
ETA: Edison Cafe - 228 W47th St (btw Bdwy & 8th Ave). Old school coffee shop/diner serving "Jewish soul food". Another big theater hang out.
Vinyl Diner - 754 9th Ave @ 51st St. I love love love the Vinyl Diner. With an eclectic menu that offers everything from 3 cheese mac & cheese to spaghetti & meatballs to pad thai to curry, there is something for everyone at this diner. The also have a fun cocktail menu.