If you're looking for a meeting place or a good stop around ½ or halfway between Shelbyville and Chattanooga, you can try Pelham, TN, which is almost an hour east of Shelbyville, or almost an hour northwest of Chattanooga.
About ¼ or a fourth of the way, you can stop at Manchester, TN. This is about half an hour east of Shelbyville.
About ⅔ or two thirds of the way, you can stop at Pinhook, TN. This is about 1 hour southeast of Shelbyville, or about half an hour west of Chattanooga.
About ¾ or three fourths of the way, you can stop at Rankin Cove, TN. This is a little over 1 hour southeast of Shelbyville, or about half an hour west of Chattanooga.
If you drive straight through without stopping at all, the total distance is 96 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 1 hour, 41 minutes.