Ok, here goes.
There's two places I can think of right off the bat.
1. Wooster Mtn - Danbury Ct. Take 84 from NY, at the mall, make the right onto rt 7 south. Proceed about 3 miles. The place is on the right. They do Trap every Tues and rifle/pistol on the weekends. I forget the annual fee, but it's modest and worth it. If you want to shoot, you must SUPPORT YOUR CLUBS AND MERCHANTS. The guys who VOLUNTEER to run both clubs are first rate! friendly and helpful. This place is strictly outdoors.
2. Putnam County Fish and Game - This place is located on Drewville Road, Carmel. Nice club offering rifle/pistol, trap, archery, hunting in season, air rifles and more. The cost is also modest. My dad is a member here. The rifle/pistol is covered but not heated.
If you like shotgun sporting clays, I'd suggest Mid Hudson Sporting Clays up in New Paltz.
Dover Furnace in Dover Plains, NY