As far as legality the answer will vary from state to state and in some places county to county within the state.
Do not come to NY with a handgun unless you are literally traveling through the state to get somewhere where you can legal possess it. And if you are doing that it should be unloaded and stored in the trunk of the vehicle or if no truck somewhere where it is not readily accessible.
In NYS no handgun possession anywhere unless you have a NYS license or you're LE or as mentioned, you're traveling through.