Truthfully I am not a fan of New York city (it is way too busy for me), but my cousin was visiting from California so I decided to make the trip out with her. We decided to take the China Town bus (www.luckystarbus.com/) because parking is a pain and cost an arm and a leg in NYC. Took the 8 AM bus and came back on the 9 PM bus for a good day trip.
In terms of food, the options in NYC are unlimited.
We ate lunch at Woorijip which had amazing quality for a good price http://www.yelp.com/biz/woorijip-new-york
We then went around Times square and did the touristy things.
Finally we had dinner at Kenka (Japanese for fight) – if you intend to go here, go early … usually the wait is about 1-2 hours! We got lucky since we came here early and only had to wait a few minutes http://www.yelp.com/biz/kenka-new-york