The fair place to meet is Indianapolis, IN — the city closest to the midpoint of Cincinnati and Louisville. From the farther side that’s about 2 hr 40 min of driving.
Recommended midpoint
Indianapolis, IN
From Cincinnati
2 hr 29 min
99 mi to Indianapolis
From Louisville
2 hr 40 min
107 mi to Indianapolis
That’s an even split — both sides drive within 11 min of each other. Cincinnati and Louisville are about 89 miles apart.
Cincinnati and Louisville are about 89 miles apart by road. Split the difference and you arrive near Indianapolis, the city closest to the halfway point between them. That splits the trip almost evenly — about 2 hr 29 min from Cincinnati and 2 hr 40 min from Louisville.
At this range, Indianapolis works for a same-day meetup: close enough from both Cincinnati and Louisville to meet for lunch or an afternoon and still be home by evening.
If Indianapolis doesn't have what you're after, Columbus and Nashville are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Cincinnati and Louisville.
Indianapolis, colloquially known as Indy, is the capital and most populous city of the U.S. state of Indiana and the county seat of Marion County. Indianapolis is situated in the state's central till plain region along the west fork of the White River. Read more →
Cincinnati is the most populous city in Hamilton County, Ohio, United States, and its county seat. Read more →
Louisville is the most populous city in the U.S. state of Kentucky, sixth-most populous city in the Southeast, and the 27th-most-populous city in the United States. Read more →
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.
Estimates use straight-line distance and typical road speeds; real drive times vary with route and traffic.