I second that response - NYC is a fab place to live, for music and many other reasons. I have a rental in midtown which is great as it's a 1 bed penthouse in an older building. I don't share a wall with anyone and the floor seems to be about 3 feet thick, so I occasionally crank it.
If you are worried about noise, try getting into a pre war apartment building, or a new one which you can thump the walls real hard - many are fire proof such that they have very solid concrete walls. Make sure you don't live in a brownstone as you can hear lots through the wooden floors. One of the other long time tenants in my building was saying how the workmen used to fill between the floors with clay - if true that stuff will absorb a lot of sound.
The pre wars also have bigger rooms I think, whereas the newer ones tend to be a bit cookie cutter. Either way it's not cheap, but I always think you should pay up for at least a couple of years to get the best out of the city - you only live once (and you don't need a car here either so that cuts the expense down).
I also have a nice pair of headphones (Senn 600s) for when I fell the need for a bit of late night listening at volume...