The fair place to meet is Kansas City, MO — the city closest to the midpoint of Denver and Nashville. From the farther side that’s about 11 hr 41 min of driving.
Recommended midpoint
Kansas City, MO
From Denver
11 hr 41 min
557 mi to Kansas City
From Nashville
9 hr 54 min
472 mi to Kansas City
Nashville has the shorter trip; the split is off by about 1 hr 47 min. The alternatives below can even it out. Denver and Nashville are about 1,020 miles apart.
Denver and Nashville are about 1,020 miles apart by road. Split the difference and you arrive near Kansas City, the city closest to the halfway point between them. That puts roughly 11 hr 41 min of driving on the Denver side and 9 hr 54 min on the Nashville side — the fairest single meeting point among the cities near the middle.
Over this distance most people will fly rather than drive the whole way. Kansas City still makes a fair, central place for Denver and Nashville to converge, splitting the travel instead of asking one side to cross the country.
If Kansas City doesn't have what you're after, Oklahoma City and Omaha are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Denver and Nashville.
Kansas City, abbreviated KC or KCMO, is the largest city in the U.S. state of Missouri by both population and area. It is located on the Missouri River at its confluence with the Kansas River, within Jackson, Clay, Platte and Cass counties. Read more →
Denver is the capital and most populous city of the U.S. state of Colorado. Officially a consolidated city and county, it is located in the South Platte River valley on the western edge of the High Plains, and is just east of the Front Range of the Rocky… 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.