If you're looking for a meeting place or a good stop around ½ or halfway between Gatlinburg and Columbus, you can try Lexington-Fayette, KY, which is about 3 hours north of Gatlinburg, or about 3 hours southwest of Columbus.
About ¼ or a fourth of the way, you can stop at Royal Blue, TN. This is a little over 1 hour northwest of Gatlinburg.
About ⅓ or a third of the way, you can stop at Grove, KY. This is almost 2 hours northwest of Gatlinburg.
About ⅔ or two thirds of the way, you can stop at Cincinnati, OH. This is about 4½ hours north of Gatlinburg, or about 2 hours southwest of Columbus.
About ¾ or three fourths of the way, you can stop at Mason, OH. This is about 5 hours north of Gatlinburg, or about 1½ hours southwest of Columbus.
If you drive straight through without stopping at all, the total distance is 397 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 6 hours, 12 minutes.