Here are few things to do around the city that won't cost you anything:
The High Museum offers free admission every first Saturday of the month to Fulton County residence.
Imagine It! children's museum has Target Free Second Tuesday on the second Tuesday every month. The museum is open for extended hours from 1-7.
Home Depot offers wonderful free workshops for children ages 5-12. They are held on the first Saturday of every month from 9:00 am - noon. The projects are really cute and in addition to the project kits the kids receive and apron.
Pottery Barn Kid stores offer free story times. Story times are held every Tuesday. Check the store nearest you for times.
They also have sing-alongs 3/11-3/13 at various locations around Atlanta. http://www.potterybarnkids.com/cust/concertseries/content.cfm