Just as a follow-up. The long guns that are illegal in NY are those that meet NY's definition of an "assault weapon". It refers to weapons with a pistol grip that extends "conspicuously" beneath the works of the gun and to those that have a magazine that holds 5 or more rounds.
NY City's Administrative Code requires that all long guns be registered with NYPD if they are kept in the City. I believe (not positive) that someone with a valid hunting license can transport a long gun unloaded and in a locked carrying case within the City limits without registering the weapon.
As far as handguns go, it is illegal for anyone who is not a law enforcement or peace officer to possess a handgun anywhere in NY State, loaded or unloaded, without a valid NY handgun license. Vendors at outdoor shows have to display handguns that have their firing mechanisms disabled in order to display their wares, as an "inoperable" firearm doesn't violate the law. Possession of an unloaded handgun is a misdemeanor and you are subject to arrest even if you have a valid license from another state. Possession of a loaded handgun is a Class D felony carrying a maximum sentence of 7 years, and a mandatory 1 year sentence unless a judge finds that imprisonment would be "unduly harsh" or there are other mitigating circumstances. If you were carrying an unloaded handgun in a carrying case with ammunition contained in the same case, the law in NY would deem that a "loaded" firearm
There are 3 types of NY handgun licenses: full carry, premises, and target/hunting. Forget about getting a full carry license anywhere in the NYC area. It's next to impossible unless you have a few thousand dollars to pay a lawyer who specializes in obtaining those permits and a year or two to wait out the court battle. Premises permits allow you to possess a handgun only on the premises where the weapon is kept. Target/hunting licenses are the easiest to obtain, and allow you to posses a handgun in your home, and to transport it unloaded to the woods or a range in a closed container. It might be possible for a non-resident to obtain a NY target/hunting handgun permit. Having a NY hunting license might be necessary. It also might help to try to obtain that license from a county that isn't adjacent to the City, as folks upstate have a slightly different view of guns
