The federal gun laws do allow you to transport a hand gun through any state, unloaded and in a lock box. But NY, being what it is, renders "through" void when you stop, even for lunch.
Long guns must be unloaded and in a commercial gun case.
The possession of any fire arm in New York City with out a New York City licence is strictly prohibited. But individuals transporting standard rifles and shot guns through the city may do so for a period of 24 hours after entering the city, if the weapons are unloaded and locked in a case.
I do recommend
Travelers Guide to Fire Arm Laws of the 50 States $14.95, if you intend to provide for your own safety. You may still travel with a fire extinguisher, tool box and band aids, for those "just in case moments". :B
Richard