I live in Monroe County (Rochester metro). Most of Western NY has no problem with handguns, but it still took me 9 months to get my permit five years ago. In NY the difficulty depends on the county you Iive in. Some are easy, some put restrictions on it, like target range only or home only and some require a training class. The closer to NYC, the harder it is. I can't speak to your county, but I bet if you ask on the NY Firearms forum someone will know.
How long have you been waiting for it?