The fair place to meet is Kansas City, MO — the city closest to the midpoint of Denver and Louisville. 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 Louisville
10 hr 3 min
479 mi to Kansas City
Louisville has the shorter trip; the split is off by about 1 hr 38 min. The alternatives below can even it out. Denver and Louisville are about 1,036 miles apart.
Denver and Louisville are about 1,036 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 10 hr 3 min on the Louisville 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 Louisville to converge, splitting the travel instead of asking one side to cross the country.
If Kansas City doesn't have what you're after, Omaha and Oklahoma City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Denver and Louisville.
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 →
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.