If you're looking for a meeting place or a good stop around ½ or halfway between Akron and Louisville, you can try Xenia, OH, which is almost 3 hours southwest of Akron, or a little over 2 hours northeast of Louisville.
About ¼ or a fourth of the way, you can stop at Steam Corners, OH. This is about 1 hour southwest of Akron.
About ⅓ or a third of the way, you can stop at Columbus, OH. This is almost 2 hours southwest of Akron.
About ⅔ or two thirds of the way, you can stop at Cincinnati, OH. This is a little over 3 hours southwest of Akron, or almost 2 hours northeast of Louisville.
About ¾ or three fourths of the way, you can stop at Florence, KY. This is almost 4 hours southwest of Akron, or a little over 1 hour northeast of Louisville.
If you drive straight through without stopping at all, the total distance is 331 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, 1 minute.