Just southwest of Atlanta, Cochran Mill Park features several waterfalls. Henry Mill Falls offers a nice little cascade at the end of a moderate hike of the yellow trail.
Cochran Mill Falls - Trip Details
For $5, you can get a parking spot at the Cochran Mill Park trailhead. The park offers a network of trails, not all of which match the map at the trailhead. So, if you have a GPS and can follow a trail on it, you may be better off.
The yellow trail is the one you want for the falls, and it takes you out and back along Bear Creek.
At 2.8 miles in, you'll reach Henry Mill Falls.
More Waterfalls around Cochran Mill Park
Cochran Mill Park and its falls are on a bit of an island as far as waterfalls go being south of Atlanta.
There is a small set of falls and cascades at Vickery Creek Falls in Roswell.
Southeast on the other side of Griffin, there is High Falls State Park which has significant flow and about a 15' total drop on the Towaliga River below High Falls Lake.