There are a bunch of ranges locally. Four Point Rod and Gun club
is great if you're into trap and skeet. They're building a 200yd rifle range as I type.
The Genesee Conservation League
has great facilities for rifle/shotgun, handgun and archery. They have an indoor range (25 yards) and a 200yd rifle range and a couple handgun ranges. They're a little pricey, but very good.
I tend to shoot on private land owned by a friend, too.
Buying long guns in Monroe County is no big deal. Just walk in, fill out a 4473, and you're good to go. If you want a handgun, you'll have to apply for a permit. It can take up to a year to get approved, which stinks, and it's not cheap. You can get more info on the Monroe County Clerk's website. There are two types of handgun permits: ownership and concealed carry. There is no open carry. If you want to carry, you should list "personal defense" on your application as a reason for applying.