If you're looking for a meeting place or a good stop around ½ or halfway between Akron and Columbus, you can try Mansfield, OH, which is almost an hour southwest of Akron, or about 1 hour northeast of Columbus.
Another possible place to stop near the midpoint is Bellville.
About ¼ or a fourth of the way, you can stop at Lodi, OH. This is about half an hour west of Akron.
About ⅓ or a third of the way, you can stop at Ashland, OH. This is almost an hour west of Akron.
About ⅔ or two thirds of the way, you can stop at Pulaskiville, OH. This is a little over 1 hour southwest of Akron, or almost an hour north of Columbus.
About ¾ or three fourths of the way, you can stop at South Woodbury, OH. This is about 1½ hours southwest of Akron, or about half an hour north of Columbus.
If you drive straight through without stopping at all, the total distance is 125 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, 57 minutes.