If you're looking for a meeting place or a good stop around ½ or halfway between Nashville and Memphis, you can try Jackson, TN, which is almost 2 hours west of Nashville, or about 1½ hours northeast of Memphis.
About ¼ or a fourth of the way, you can stop at Graham, TN. This is almost an hour southwest of Nashville.
About ⅓ or a third of the way, you can stop at Cedar Grove, TN. This is almost an hour west of Nashville.
About ⅔ or two thirds of the way, you can stop at Brownsville, TN. This is a little over 2 hours west of Nashville, or about 1 hour northeast of Memphis.
About ¾ or three fourths of the way, you can stop at Birds Bower, TN. This is about 2½ hours west of Nashville, or almost an hour northeast of Memphis.
If you drive straight through without stopping at all, the total distance is 212 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 3 hours, 11 minutes.