It depends on which theater I plan to go to. Other posters have already listed some of my favorites (Bar Centrale, Cafe un deux trois, becco, dickens, dutch fred's, etc.)
The bar my friends and I went to after watching Heart of Rock n Roll is called Woo Woo lounge. It's an 80s speakeasy cocktail bar on 47th street between Broadway and 8th avenue (right next to Mean Fiddler bar and SIX musical). You need to go to their website to get the passcode to enter. I've taken friends from out of town here so they get the idea of what NYC was like back in the 80s and everyone has had a great time. Cocktails are $18 though so not the cheapest.
Din Tai Fun is opening in NYC July 11. Right across the street from the Winter Garden. Famous dumplings, I’ve been to the one in Seattle, very popular place.
I make a visit to 44 & X (yes it’s at 44th and 10th avenue) on all of my theater trips. It has a great food menu and the cocktail menu is fun as all the drinks are named after Broadway shows. The location is great for dining prior to shows located on 44th/45th streets.
My new favorite spot is Spice Symphony. It is a delicious Indian/Chinese place. There is a location in UES as well as right off Times Square on I think 46th street. Delicious!!!
Broadway Flash said: "Has anyone ever gone to FrikiTiki? How is it?It looks like it’s owned by the head of seaview."
I enjoyed it there, the piano player is fun and has a great rapport with the audience (I dont' remember which one since I think there's multiple) and it's just a good vibe throughout, though a bit loud if you want to actually have conversation. I wasn't obsessed with any of their specialty cocktails but they weren't bad, and the food is good enough for light bar bites. I know they had a partnership with Natalie Joy Johnson to do some themed nights when she was in Lempicka, so I think it would be cool if they did more of that.
On my first real trip to New York in college, we stayed on the Hotel Edison, which was next door to Carve, on the corner of 47th and 8th. An over-the-counter place, they sell Pizza by the slice, Egg on a roll, that kind of thing. I was a broke college kid, so it was the only place I could afford to eat at during the trip. I can afford to eat at much nicer places now, but Carve's got sentimental value, so every time I'm in New York, I make it a point to stop at Carve and grab a slice of pizza or a piece of pie before I see a show.