You would probably be better off heading to North Carolina and the Smoky Mountains. The southern section of the Blue Ridge Parkway has some relatively high elevation sections (for the eastern US), 5000 to 6000 feet. Elevation is your only relief from summer heat in the SE. Depending where you are in Atlanta, you are about four hours from this part of the Parkway.

Rough rule of thumb is 6 to 8 degrees cooler for every 1000 feet in elevation. So when Atlanta is 94F, parts of the parkway will be more like 70F. Waynesville at about 2800 feet elevation has average high in August of 82, low of 56, versus 88 F high, 70 F low in Atlanta. The mountain areas you refer to in GA are not as hot, but the mountains of Georgia do not have the elevations of North Carolina.