The fair place to meet is Cleveland, OH — the city closest to the midpoint of Buffalo and Indianapolis. From the farther side that’s about 5 hr 31 min of driving.
Recommended midpoint
Cleveland, OH
From Buffalo
3 hr 38 min
173 mi to Cleveland
From Indianapolis
5 hr 31 min
263 mi to Cleveland
Buffalo has the shorter trip; the split is off by about 1 hr 53 min. The alternatives below can even it out. Buffalo and Indianapolis are about 435 miles apart.
Buffalo and Indianapolis are about 435 miles apart by road. Split the difference and you arrive near Cleveland, the city closest to the halfway point between them. That puts roughly 3 hr 38 min of driving on the Buffalo side and 5 hr 31 min on the Indianapolis side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Cleveland suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Cleveland doesn't have what you're after, Detroit and Columbus are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Buffalo and Indianapolis.
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 →
Buffalo is a city in the U.S. state of New York. It lies in Western New York on the eastern shore of Lake Erie and at the head of the Niagara River on the Canada–United States border. 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.