Atlanta and Charlotte are about 226 miles apart by road. Split the difference and you arrive near Raleigh, the city closest to the halfway point between them. That puts roughly 7 hr 27 min of driving on the Atlanta side and 3 hr 15 min on the Charlotte side — the fairest single meeting point among the cities near the middle.
At this range, Raleigh works for a same-day meetup: close enough from both Atlanta and Charlotte to meet for lunch or an afternoon and still be home by evening.
If Raleigh doesn't have what you're after, Birmingham and Nashville are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Atlanta and Charlotte.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.