The fair place to meet is Kansas City, MO — the city closest to the midpoint of Memphis and Minneapolis. From the farther side that’s about 8 hr 38 min of driving.
Recommended midpoint
Kansas City, MO
From Memphis
7 hr 45 min
370 mi to Kansas City
From Minneapolis
8 hr 38 min
412 mi to Kansas City
Memphis has the shorter trip; the split is off by about 53 min. The alternatives below can even it out. Memphis and Minneapolis are about 700 miles apart.
Memphis and Minneapolis are about 700 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 7 hr 45 min of driving on the Memphis side and 8 hr 38 min on the Minneapolis 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, Omaha and Chicago are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Memphis and Minneapolis.
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 →
Minneapolis is a city in Hennepin County, Minnesota, United States, and its county seat. With a population of 429,954 as of the 2020 census, it is the state's most populous city. 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.