Traffic in NYC isn't nearly as bad as you would think. Most of it is slow like you say, and believe it or not, drivers do watch for you. The bike lanes are everywhere too now so you can always find one for a long portion of your route. My commute is 10 miles from Brooklyn to 42nd St in Manhattan and only the short stretch from my house into Prospect Park on the suburban-like residential streets for under a mile, and then two short blocks after the bridge in Manhattan are off cycle lanes. All the rest is on bike routes, much of it dedicated.
I'd recommend a trip up the west side greenway and of course Central Park for a bike ride in Manhattan if you were just looking to ride. And of course Citibike is everywhere now.