Bullseye indoor range and gunshop
Not exactly sure how close to Atlanta it is, but I think its in Marietta. Wish I could be more specific, but I can tell you I always make it a point to go there when visiting my family members living in the Atlanta area, being a visitor, I am not driving, they just take me there.
They have a very good selection of handgun rentals and Class III rentals including UZI, MP5, Thompson, etc. Prices are reasonable too, when I was there during Thanksgiving weekend, range time was $10 per shooter per lane, no time limit, eye and ear protection cost a buck each, but if you rent guns you have to shoot thier ammo, fairly priced at only $12 per 50 for 9MM last time I was there. Pistols and machine guns both rented at $10 each regardless of type or caliber, no time limit on them either last time I was there.
They are by far the most reasonably priced indoor range I have ever visited.