It depends on if you are getting a refund or not. See below from https://dor.georgia.gov/mailing-address-individualfiduciary-income-tax
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
500X Amended
Georgia Dept. of Revenue
PO Box 740318
Atlanta, GA 30374-0318