If you're looking for a meeting place or a good stop around ½ or halfway between Atlanta and Morristown, you can try Cleveland, TN, which is about 2 hours north of Atlanta, or about 2 hours southwest of Morristown.
Another possible place to stop near the midpoint is East Brainerd.
About ¼ or a fourth of the way, you can stop at Calhoun, GA. This is almost an hour northwest of Atlanta.
About ⅓ or a third of the way, you can stop at Dalton, GA. This is a little over 1 hour northwest of Atlanta.
About ⅔ or two thirds of the way, you can stop at Lenoir City, TN. This is almost 3 hours north of Atlanta, or a little over 1 hour southwest of Morristown.
About ¾ or three fourths of the way, you can stop at Knoxville, TN. This is about 3 hours north of Atlanta, or almost an hour southwest of Morristown.
If you drive straight through without stopping at all, the total distance is 261 miles. The distances shown above don't include local roads to get into each town, so if you're planning a long road trip, make sure you factor in traffic and road conditions, rest stop breaks, and interesting detours along the way. If you're in a rush, you can do the trip with zero stops, and your total travel time would be around 3 hours, 57 minutes.