The fair place to meet is Indianapolis, IN — the city closest to the midpoint of Chicago and Nashville. From the farther side that’s about 5 hr 16 min of driving.
Recommended midpoint
Indianapolis, IN
From Chicago
3 hr 27 min
165 mi to Indianapolis
From Nashville
5 hr 16 min
251 mi to Indianapolis
Chicago has the shorter trip; the split is off by about 1 hr 49 min. The alternatives below can even it out. Chicago and Nashville are about 398 miles apart.
Chicago and Nashville are about 398 miles apart by road. Split the difference and you arrive near Indianapolis, the city closest to the halfway point between them. That puts roughly 3 hr 27 min of driving on the Chicago side and 5 hr 16 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 Indianapolis suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Indianapolis doesn't have what you're after, Louisville and Cincinnati are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Chicago and Nashville.
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 →
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 →
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.