No problems with rifles outside the city. New York State's assault rifle ban is pretty much a mirror of the feds-but ours will still be here in 2004.
I'd have to look at the city statute to be sure, but basically in the city-no pistols no assault rifles, I think you can get some kind of permit to have other long guns in the city-if your interested I could dig that up...
Outside the City
Pistols require a permit. The actual law states that there are carry and, I think, premises permits (everyone I know has carry). However the permit is issued by the senior county court judge in the county you live and some "restrict" the permit-they write "for hunting only" or "for target shooting only." You could probably not be convicted for criminal possession of a weapon for carrying outside the permit restriction, but you would certainly get your pistols taken away and your permit yanked. Some counties also require training clases and some restrict the pistols you can have-have to ask a local gun shop or whoever handles pistols permits-county clerk upstate (where I live), don't know about downstate.