I agree with the others that most of the really good golf here is at the private clubs, but there is some really good public and semi-private clubs here.
Just some suggestions.....
Town Lake Hills, Bridge Mill, Stone mountain, Mystery Valley, Echelon, Reunion, Chateau Elan, The Frog, are just a sampling of what I consider good to excellent local venues. If you don't mind driving a bit, Callaway Gardens has some great golf, and to the west of the city, there are tons of courses in the Lake Oconee area.
Good luck in planning your trip!