I've been living and locking in NYC for years.
If I'm going to be leaving my bike outside for a while it gets the big U Lock. If I were doing it in the same place day after day, it would get the chain around both wheels and the frame. But most of the time I just use my mini U. When I was occasionally riding my Pog and Felt around town I'd manage to get the Big U through the front wheel, downtube, and LOOK pedal - which was kind of like locking up the rear wheel.
There are some places where I hate locking up, but usually I'm locking up with my sweetheart. Two bikes, two mini Us, plus a cable through the wheels is all we usually do.
Once you live in NYC, be as careful as you need to until you get a sense of where you should and shouldn't. Don't lock up in Union Square. Don't lock up to scaffolding. If you're everydaying it, make friends with the guy in the coffee cart fifteen feet away and tell him not to let anyone mess with your bike. Lock up near other bikes, and have a better lock. Thieves are pretty opportunistic and indiscriminate. They did not steal your bike because it was nice. They stole it because it was easy to steal.
Lots of bikes have been recovered, so if yours gets pinched, tell all the bike shops roughly in the area, spread the word, and there's a chance that you'll get it back. A teammate of mine just got his track bike back after like eight months. A guy I worked with got his back after four or five months. And I can probably think of like four or six others where the word had been spread, the bike had been spotted, and good folks stepped up to help out. Bikes returned to owners, sometimes giving forty or sixty bucks to whatever poor sucker was riding it. They didn't steal it, they just bought it 'cause they needed it and didn't know better.