The fair place to meet is Columbus, OH — the city closest to the midpoint of Detroit and Louisville. From the farther side that’s about 3 hr 58 min of driving.
Recommended midpoint
Columbus, OH
From Detroit
3 hr 26 min
164 mi to Columbus
From Louisville
3 hr 58 min
189 mi to Columbus
Detroit has the shorter trip; the split is off by about 32 min. The alternatives below can even it out. Detroit and Louisville are about 316 miles apart.
Detroit and Louisville are about 316 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 26 min of driving on the Detroit side and 3 hr 58 min on the Louisville 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 Indianapolis are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Detroit and Louisville.
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 →
Detroit is the most populous city in the U.S. state of Michigan. It is situated on the bank of the Detroit River across from the Canadian city of Windsor, Ontario. It is the 26th-most populous city in the United States and the largest U.S. Read more →
Louisville is the most populous city in the U.S. state of Kentucky, sixth-most populous city in the Southeast, and the 27th-most-populous city in the United States. 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.