Have fun! I was just there last December for a few days. What part are you staying in? That plays a huge role in where you will/should visit. I stayed in Brooklyn and the subway right was a BIT long and crowded at times to Manhattan, but it was worth it.
The best restaurant I went to there was Momofuku Noodle Bar. The best cafe (and probably my favorite place in NYC) was
House Of Small Wonder. Seriously, check it out if you can.
Definitely check out the 9/11 memorial. It's usually busy, but is worth it. There's a lot to do/see nearby, too. Look up free NYC attractions. Different attractions have "free" days.
Chinatown is awesome, too!