If you're looking for a meeting place or a good stop around ½ or halfway between Detroit and Mount Vernon, OH, you can try Findlay, OH, which is almost 2 hours south of Detroit, or almost 2 hours northwest of Mount Vernon, OH.
Another possible place to stop near the midpoint is Digby.
About ¼ or a fourth of the way, you can stop at Toledo, OH. This is almost an hour southwest of Detroit.
About ⅔ or two thirds of the way, you can stop at Lovell, OH. This is about 2 hours south of Detroit, or a little over 1 hour northwest of Mount Vernon, OH.
About ¾ or three fourths of the way, you can stop at Marion, OH. This is about 2½ hours south of Detroit, or almost an hour west of Mount Vernon, OH.
If you drive straight through without stopping at all, the total distance is 210 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, 25 minutes.