I am interested in going to a range to shoot both hand guns and rifles while in Georgia. Is it legal to do this in Georgia as a non-resident, and if it is legal, is it common for ranges to deny entry to non-residents?
It is absolutely legal to shoot at a range as long as you either shoot their guns or bring your own legal firearm to the range provided your weapon meet range's restrictions.
Normally the only thing that you need to have with you is a valid photo ID.
You can probably use Where to Shoot Site to limit the list of shooting ranges.