I am actually going to see The Producers this saturday.
The empire state building really is a sight to see. I've gone to the top twice, both at night, and it was amazing. This is not to miss even if you have a fear of heights. I do and my fear didn't bother me once.
Central Park is beautiful. It is truly amazing how in a large city there is such a wonderful park. If the weather is permitting you can rent a rowboat and row around the larger lake there. Just remember, this park is HUGE!
5th avenue. How can you not walk down there, at least once. Cartier? Armani? All the great stores and the World of Disney all withing a short walking distance.
Macy's! It is unbelievably huge. Even if you don't want to shop, take the escalators up to the 8th floor. You'll notice that they are quite old....and wooden!
ETA: The Brooklyn Bridge. If it is a nice day out you may want to walk across the bridge. Not maybe people think to do this but it is very cool. And right at the end is City Hall. It is a nice place to sit and they have a beautiful fountain.
There are many cool places to eat. Bubba Gumps Shrimp is not overly priced, right in Times Square, and has good food. Jekyll and Hyde (on 59th or 57th) is a really cool themed restaurant. It is a little pricey but they really get into the whole show. Mars2112 is another themed restaurant. It is definitely geared towards younger kids and the menu is very limited but it is fun. And for the parents there is always Tequilaville.
And just remember to wear comfortable shoes, take lots of pictures, and don't touch things. Have fun!