Please see the below for the Georgia Department of Revenue mailing addresses (they are also printed right above the signature line of your Georgia return):
500 and 500 EZ (refunds and no balance due)
Georgia Dept. of Revenue
PO Box 740380
Atlanta, GA 30374-0380
500 and 500 EZ (payments)
Georgia Dept. of Revenue
PO Box 740399
Atlanta, GA 30374-0399