The fair place to meet is Cleveland, OH — the city closest to the midpoint of Buffalo and Cincinnati. From the farther side that’s about 4 hr 40 min of driving.
Recommended midpoint
Cleveland, OH
From Buffalo
3 hr 38 min
173 mi to Cleveland
From Cincinnati
4 hr 40 min
222 mi to Cleveland
Buffalo has the shorter trip; the split is off by about 1 hr 2 min. The alternatives below can even it out. Buffalo and Cincinnati are about 393 miles apart.
Buffalo and Cincinnati are about 393 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 4 hr 40 min on the Cincinnati 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, Pittsburgh and Columbus are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Buffalo and Cincinnati.
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 →
Cincinnati is the most populous city in Hamilton County, Ohio, United States, and its county seat. 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.