If you're looking for a meeting place or a good stop around ½ or halfway between Shelbyville and Gatlinburg, you can try Crossville, TN, which is a little over 2 hours east of Shelbyville, or about 2 hours west of Gatlinburg.
About ¼ or a fourth of the way, you can stop at Big Spring, TN. This is a little over 1 hour north of Shelbyville.
About ⅓ or a third of the way, you can stop at Carthage, TN. This is a little over 1 hour northeast of Shelbyville.
About ⅔ or two thirds of the way, you can stop at Dochester, TN. This is about 2½ hours east of Shelbyville, or about 1½ hours west of Gatlinburg.
If you drive straight through without stopping at all, the total distance is 247 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 4 hours, 16 minutes.