The fair place to meet is Columbus, OH — the city closest to the midpoint of Cleveland and Indianapolis. From the farther side that’s about 3 hr 31 min of driving.
Recommended midpoint
Columbus, OH
From Cleveland
3 hr 9 min
126 mi to Columbus
From Indianapolis
3 hr 31 min
168 mi to Columbus
Cleveland has the shorter trip; the split is off by about 22 min. The alternatives below can even it out. Cleveland and Indianapolis are about 263 miles apart.
Cleveland and Indianapolis are about 263 miles apart by road. Split the difference and you arrive near Columbus, the city closest to the halfway point between them. That puts roughly 3 hr 9 min of driving on the Cleveland side and 3 hr 31 min on the Indianapolis side — the fairest single meeting point among the cities near the middle.
At this range, Columbus works for a same-day meetup: close enough from both Cleveland and Indianapolis to meet for lunch or an afternoon and still be home by evening.
If Columbus doesn't have what you're after, Cincinnati and Detroit are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Cleveland and Indianapolis.
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 →
Cleveland is a city in the U.S. state of Ohio and the county seat of Cuyahoga County. Located along the southern shore of Lake Erie, it is situated across the lake from Ontario, Canada, and is approximately 60 miles west of the Ohio–Pennsylvania state line. Read more →
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 →
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.