If you're looking for a meeting place or a good stop around ½ or halfway between Atlanta and Hendersonville, you can try Ebenezer, TN, which is about 2 hours northwest of Atlanta, or about 2 hours southeast of Hendersonville.
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 Tullahoma, TN. This is almost 3 hours northwest of Atlanta, or a little over 1 hour south of Hendersonville.
About ¾ or three fourths of the way, you can stop at Murfreesboro, TN. This is about 3 hours northwest of Atlanta, or almost an hour south of Hendersonville.
If you drive straight through without stopping at all, the total distance is 265 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, 59 minutes.