The fair place to meet is Oklahoma City, OK — the city closest to the midpoint of Kansas City and Memphis. From the farther side that’s about 8 hr 50 min of driving.
Recommended midpoint
Oklahoma City, OK
From Kansas City
6 hr 15 min
298 mi to Oklahoma City
From Memphis
8 hr 50 min
422 mi to Oklahoma City
Kansas City has the shorter trip; the split is off by about 2 hr 35 min. The alternatives below can even it out. Kansas City and Memphis are about 370 miles apart.
Kansas City and Memphis are about 370 miles apart by road. Split the difference and you arrive near Oklahoma City, the city closest to the halfway point between them. That puts roughly 6 hr 15 min of driving on the Kansas City side and 8 hr 50 min on the Memphis side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Oklahoma 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 Oklahoma City doesn't have what you're after, Nashville and Omaha are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Kansas City and Memphis.
Oklahoma City, often shortened to OKC, is the capital and most populous city in the U.S. state of Oklahoma. It is the 21st-most populous U.S. city and 8th largest in the Southern United States, with a population of 681,054 at the 2020 census. Read more →
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 →
Memphis is a city in Shelby County, Tennessee, United States, and its county seat. 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.