NYC has its own set of gun laws - I don't have the statute handy, but absolutely no assault weapons (as defined under federal law). In fact, I don't think you can get anything that even has the ability to accept a hi-cap mag (so not even post ban AR15's, FAL's, etc). Bolt action hunting rifles are allowed, as are some shotguns, but you need to get a permit to merely have them in your home. There's three types of pistol permits. One to just keep it in your home, one to carry back and forth to the range, and the third is actually a CCW. To get the CCW you need to be a celeb or carrying large sums of money on a weekly basis (I've heard its $10k per week deposits). Its VERY difficult to get any type of pistol permit in the city, the CCW is next to impossible unless you're Donald Trump or Howard Stern. Absolutely no class three stuff in the state unless you're a manufacturer or importer and you have some really heavy duty contacts at BATF.
Basicly, if you're moving to NYC, store your guns in another state and forget about CCW. NYC's laws make California look like Arizona or Texas.
And drop me an email when you get up here - lets get a beer.