The fair place to meet is Chicago, IL — the city closest to the midpoint of Minneapolis and Nashville. From the farther side that’s about 8 hr 20 min of driving.
Recommended midpoint
Chicago, IL
From Minneapolis
7 hr 26 min
355 mi to Chicago
From Nashville
8 hr 20 min
398 mi to Chicago
Minneapolis has the shorter trip; the split is off by about 54 min. The alternatives below can even it out. Minneapolis and Nashville are about 697 miles apart.
Minneapolis and Nashville are about 697 miles apart by road. Split the difference and you arrive near Chicago, the city closest to the halfway point between them. That puts roughly 7 hr 26 min of driving on the Minneapolis side and 8 hr 20 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 Chicago suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Chicago doesn't have what you're after, Milwaukee and Indianapolis are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Minneapolis and Nashville.
Chicago is the most populous city in the U.S. state of Illinois and in the Midwestern United States. Located on the western shore of Lake Michigan, it is the third-most populous city in the United States, with a population of 2.74 million at the 2020 census. Read more →
Minneapolis is a city in Hennepin County, Minnesota, United States, and its county seat. With a population of 429,954 as of the 2020 census, it is the state's most populous city. 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.