Easiest (and probably most cost effective) way to see New York is to do the double-decker tour bus thing. It's a real touristy thing to do...but hey, that's what you are. It takes you everywhere and you can get on or off as many times and at as many places as you want.
Here's the link:
http://www.coachusa.com/newyorksightseeing/
Too many great places to eat to name...just ask around based on what you're in the mood for and you'll get plenty of suggestions.