Absolutely.
NY State consists of 62 counties which includes Manhattan and the 'five boroughs'. Hunting and fishing laws and licenses are administered by the state but has specific rules per county mostly related to population.
In the more densely populated counties like the one I live in it's no rifles. Deer and bear can be taken with shotguns with slugs or handguns that are minimum 6" barrel length, minimum .357 Magnum cartridge. Bows and muzzle loaders have different, longer seasons.
Drive an hour north of here and you can use rifles. When I say 'howling wilderness' I ain't kidding. I am trying to find a way to give you a sense of scale. Dive 90 minutes north of here and you're in Adirondak Park. You'd still be in it three hours later at highway speeds and when you get far enough north the road signage is in French.
In terms of square miles you could plunk Yorkshire and Argyll Counties into it and have room left over for a number of the very small ones. Adirondak Park is roughly 16% of the total square mileage of the state.
That's the kind of big and empty I am talking about. Very rugged hilly country, lots of dark deep gorges, heavily forested. Plenty of Sasquatch no doubt .....