The fair place to meet is Kansas City, MO — the city closest to the midpoint of Louisville and Omaha. From the farther side that’s about 10 hr 3 min of driving.
Recommended midpoint
Kansas City, MO
From Louisville
10 hr 3 min
479 mi to Kansas City
From Omaha
3 hr 28 min
165 mi to Kansas City
Omaha has the shorter trip; the split is off by about 6 hr 35 min. The alternatives below can even it out. Louisville and Omaha are about 579 miles apart.
Louisville and Omaha are about 579 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 10 hr 3 min of driving on the Louisville side and 3 hr 28 min on the Omaha side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Kansas City suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Kansas City doesn't have what you're after, Chicago and Indianapolis are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Louisville and Omaha.
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 →
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 →
Omaha is the most populous city in the U.S. state of Nebraska. It is located in the Midwestern United States along the Missouri River, about 10 mi (15 km) north of the mouth of the Platte 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.