You're better off looking in Statesboro. If you're stationed on Stewart check at the on post fish and game office to see if you can occupy a zone for recreational shooting with your game license. You could use the artillery impact area as a backstop. Downside is that area can be pretty dense.
It might also be worth your time to go down to HAAF and join the Mossy Oak gun club at the MWR skeet range. That would be a good place to network with other shooters.