If you're looking for a meeting place or a good stop around ½ or halfway between Shelbyville and Asheville, you can try Hidden Hollow Estates, TN, which is about 2½ hours east of Shelbyville, or almost 3 hours west of Asheville.
About ¼ or a fourth of the way, you can stop at Cherry Valley, TN. This is about 1 hour north of Shelbyville.
About ⅓ or a third of the way, you can stop at Cookeville, TN. This is about 1½ hours northeast of Shelbyville.
About ⅔ or two thirds of the way, you can stop at Sevierville, TN. This is about 3½ hours east of Shelbyville, or about 1½ hours west of Asheville.
About ¾ or three fourths of the way, you can stop at Sandy Ridge, TN. This is almost 4 hours east of Shelbyville, or about 1½ hours northwest of Asheville.
If you drive straight through without stopping at all, the total distance is 321 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 5 hours, 2 minutes.