I live in Buffalo, NY (which is about 9 hours from NYC) and I went to NYC for the first time this April on a trip for band. It was so much fun. I highly reccomend that you see a broadway show. We saw Chicago at the Ambassador Theater. It was really cool because our first chair trumpet player and percussionist actually got to play in the pit orchestra.
Exploring China Town was really fun, but pretty scary at night.
Have a great trip to the Big Apple and an amazing cruise!