The fair place to meet is Indianapolis, IN — the city closest to the midpoint of Cincinnati and Columbus. From the farther side that’s about 3 hr 31 min of driving.
Recommended midpoint
Indianapolis, IN
From Cincinnati
2 hr 29 min
99 mi to Indianapolis
From Columbus
3 hr 31 min
168 mi to Indianapolis
Cincinnati has the shorter trip; the split is off by about 1 hr 2 min. The alternatives below can even it out. Cincinnati and Columbus are about 100 miles apart.
Cincinnati and Columbus are about 100 miles apart by road. Split the difference and you arrive near Indianapolis, the city closest to the halfway point between them. That puts roughly 2 hr 29 min of driving on the Cincinnati side and 3 hr 31 min on the Columbus side — the fairest single meeting point among the cities near the middle.
At this range, Indianapolis works for a same-day meetup: close enough from both Cincinnati and Columbus to meet for lunch or an afternoon and still be home by evening.
If Indianapolis doesn't have what you're after, Louisville and Cleveland are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Cincinnati and Columbus.
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 →
Columbus is the capital and most populous city of the U.S. state of Ohio. With a population of 905,748 at the 2020 census, it is the 14th-most populous city in the U.S., second-most populous city in the Midwest, and third-most populous U.S. state capital. 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.