If you're looking for a meeting place or a good stop around ½ or halfway between Gatlinburg and Seymour Heights, you can try New Era, TN, which is about half an hour northwest of Gatlinburg, or about half an hour east of Seymour Heights.
About ¼ or a fourth of the way, you can stop at Pigeon Forge, TN. This is about 11 minutes northwest of Gatlinburg.
About ⅓ or a third of the way, you can stop at Pine Grove, TN. This is about 15 minutes northwest of Gatlinburg.
If you drive straight through without stopping at all, the total distance is 24 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 44 minutes.