The fair place to meet is Columbus, OH — the city closest to the midpoint of Buffalo and Nashville. From the farther side that’s about 6 hr 59 min of driving.
Recommended midpoint
Columbus, OH
From Buffalo
6 hr 10 min
294 mi to Columbus
From Nashville
6 hr 59 min
333 mi to Columbus
Buffalo has the shorter trip; the split is off by about 49 min. The alternatives below can even it out. Buffalo and Nashville are about 627 miles apart.
Buffalo and Nashville are about 627 miles apart by road. Split the difference and you arrive near Columbus, the city closest to the halfway point between them. That puts roughly 6 hr 10 min of driving on the Buffalo side and 6 hr 59 min on the Nashville side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Columbus suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Columbus doesn't have what you're after, Cincinnati and Cleveland are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Buffalo and Nashville.
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 →
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 →
Nashville is the capital and most populous city in the U.S. state of Tennessee. It is the seat of Davidson County in Middle Tennessee, located on the Cumberland 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.