I just moved to NYC. Big fan so far. As everyone has said, most of it NYC is safe/interesting/fun. You'll know pretty quickly if you are somewhere where you probably shouldn't be.
I think the key to integrating into NY is to work on your blank stare. You'll use this all over the city, but particularly in the subway. It's a zombie-like forward stare, but be careful not to make eye contact with anyone. Eyes can be a little glazed over, but you must be somewhat alert. The goal is to make yourself look as soul-less as possible. Once you develop this, I'm pretty sure you are 95% of the way to being seen as a New Yorker.