If you're looking for a meeting place or a good stop around ½ or halfway between Finneytown and Lorain, you can try Dublin, OH, which is about 2 hours northeast of Finneytown, or about 2 hours southwest of Lorain.
Another possible place to stop near the midpoint is Westerville.
About ¼ or a fourth of the way, you can stop at Xenia, OH. This is almost an hour northeast of Finneytown.
About ⅓ or a third of the way, you can stop at Grove City, OH. This is about 1½ hours northeast of Finneytown.
About ⅔ or two thirds of the way, you can stop at Mansfield, OH. This is almost 3 hours northeast of Finneytown, or a little over 1 hour south of Lorain.
If you drive straight through without stopping at all, the total distance is 225 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, 53 minutes.