Travelling to NYC

[Uru-Nitro]

Hello, I’m travelling to NYC in March for a week. It’s my first time in the US, and I’m going to stay basically in Manhattan. I wonder if you could point me some nice places to visit. Not just the famous buildings (empire state, liberty island, ground zero…), but local places like markets, music stores, squares or whatever you find interesting to see the city life.

I’m also thinking about attending to a NBA game. The one I can go is Nets vs Bulls, which looks pretty good, but I don’t know if it’s worth and safe going to Brooklyn in subway by night and getting back the same way.
I know I might sound a bit paranoid, but here in Europe we have a very violent image of the US with all that movies and TV series.

Anyway, thank you very much for your time, all advices will be appreciated!