Relax and enjoy your riding in NYC. I don't find it bad at all. If you haven't visited that city in a while, you'll be surprised at just how tame the traffic has become. It is now against the law to lay on your horn. You'll hear some short honking, occasionally a renegade horn-blower, but, in general, folks have learned to drive in NYC without all the noise and obnoxiousness that used to be the norm. Things seem a lot cleaner to me, these days. The city is no more (perhaps even less) crime ridden than many. I would not hesitate to ride the subways most anywhere in NYC.
Also, I second the advice to visit the bridges if you have time. The Brooklyn Bridge is just fantastic - great view and the bridge design will impress you. GWB will give you a spectacular view back down the river at Manhattan. You can cross out of NYC into NJ and ride up Route 9, I think it is, along the rim of the Hudson. You'll see some absolutely beautiful scenery.
All in all, it is just a great place to ride a bike. Have fun, and report back to us on your experience.
Caruso