There are so many places to eat in the theatre district that keeping up with them would be a full time job.
There is something for everyone and every budget from Mickey D's on up into the $tratosphere. Plus there is a huge variety of cuisine.
A good place to start would be Restaurant Row which is W. 46th between 8th and 9th Aves. There are about 20 restaurants on that block alone. On 9th Avenue is another plethora of places to eat although they are not as heavily concentrated as Restaurant Row.
Eating in NY is not a problem. It is almost a contact sport however because we all do it a lot.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher