The fair place to meet is Kansas City, MO — the city closest to the midpoint of Nashville and Omaha. From the farther side that’s about 9 hr 54 min of driving.
Recommended midpoint
Kansas City, MO
From Nashville
9 hr 54 min
472 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 26 min. The alternatives below can even it out. Nashville and Omaha are about 606 miles apart.
Nashville and Omaha are about 606 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 9 hr 54 min of driving on the Nashville 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, Memphis and Indianapolis are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Nashville 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 →
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 →
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.