If you're looking for a meeting place or a good stop around ½ or halfway between Finneytown and Lake Station, you can try Brownsburg, IN, which is about 2 hours northwest of Finneytown, or about 2 hours south of Lake Station.
Another possible place to stop near the midpoint is Lebanon.
About ¼ or a fourth of the way, you can stop at Shelbyville, IN. This is about 1 hour west of Finneytown.
About ⅓ or a third of the way, you can stop at Indianapolis, IN. This is about 1½ hours northwest of Finneytown.
About ¾ or three fourths of the way, you can stop at Round Grove, IN. This is about 3 hours northwest of Finneytown, or about 1 hour south of Lake Station.
If you drive straight through without stopping at all, the total distance is 261 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, 59 minutes.