We camped at Stone Mountain several years ago and had a great time. There is a LOT to do there...and it was really very affordable.
When we camped, we were able to get wristbands which got us in to almost all of the attractions...in fact, it seemed like if you bought the wristbands after a certain time, you could use them for a day and a half....some of the things the wristband covered were the cable car, mini-golf, water slides, paddlewheel boat cruise, train ride, plantation house, and antique car museum.
The section of the campground we stayed in was very nice...very hilly terrain right on the lake...bathhouses were nice.
We went to the laser show almost every night...pack food and eat dinner on the Great Lawn before the show...is a really great atmosphere.
There is also a "town" adjacent to the Great Lawn which has a "feel" similar to Dollywood.
http://stonemountainpark.com/
Six Flags Amusement Park and Whitewater water park are some options...as well as the Georgia Aquarium and World of Coke.
Our kids also really enjoyed the Cyclorama
http://www.atlantacyclorama.org/