If you visit on your own, you will find plenty to do. Ask for a scavenger hunt list at the front desk, and meet the animals when the handlers feed them or give talks about them. You can bring a picnic lunch to eat outside.
But don't miss the scheduled events. Each year there are festivals: Earth Day, Butterfly, and Halloween. Get out on the Chattahoochee with naturalist-led canoe trips. Little kids can sign up for preschool adventures, storytimes, animal breakfasts or infant walks. Older children can visit Starlab, a portable planetarium, or experience nocturnal animals on night hikes. CNC is also a popular place for birthday parties, and their summer day camp, Camp Kingfisher, is immensely popular.
Good to know: Chattahoochee Nature Center is open from 9:00-5:00 M-Sa and 12:00-5:00 Su, except for Christmas, New Year's Day, and Thanksgiving. The cost is $8.00 for adults; $5.00 for ages 3-12; and free for ages 2 and under. A family membership costs $75, which includes 10 guest passes. If you plan to attend many scheduled events or live close by, membership would be well worth it.