Step outside Atlanta and drive over to Athens, home of UGA, REM and Bear Hollow Zoo. Admission is free. On the weekends, you can check out the exhibit hall, which usually has projects for younger kids. You might not get to visit with pandas or more exotic animals, but there are plenty of animals native to the state at the zoo and wild animals that you can touch.
Hartwell Hwy, Elberton, GA 30635
Take a drive to Elberton for one of the most interesting spots in the state, the Georgia Guidestones. Commissioned anonymously in the late-70s, the Guidestones are Georgia's version of Stonehenge. There are 10 guidelines inscribed on the granite monument, in eight modern languages, and a smaller message on the top of it in four ancient languages. Another stone tablet to the west gives notes on the history and purpose of the Guidestones. You pay only what it costs to get you there; there's no fee for visiting the Guidestones.
Monastery of the Holy Spirit
2625 GA-212, Conyers, Ga 30094
Hidden in Conyers, this active monastery is home to 40 Trappist monks and a lot of interesting history. Take your camera and photograph the beautiful buildings, walk down to the pond and feed the ducks, or check out the new visitor's center where you can learn about the history of the Trappist monks. There's also a cafe, a garden center, the Abby Store and a bonsai garden to enjoy. The visit is free, though there are things to purchase there if you're so inclined.
Young Eagles Fly Again
If your child is at least 8, he or she can take part in the Young Eagles Fly Again program. In various cities across the state, licensed pilots will give a basic aviation course and then take your child up to show her the sites from a plane. The flights are free and focus on teaching children that the sky really is the limit for them.
Folk Art Garden
1411 Rome Rd., Calhoun, Ga 30701
This is another freebie that kids of all ages will love. Nestled behind a church in Calhoun, there's a folk art garden that stretches for about an acre all through a beautiful garden. Small structures were painstakingly made with pebbles and glass beads to form castles and small buildings. There are about 50 structures to look at – some with intricate stained glass windows, others shaped like little Hobbit holes. It's a whimsical trip that costs only gas and time.