Los Angeles and Minneapolis are about 1,521 miles apart by road. Split the difference and you arrive near Denver, the city closest to the halfway point between them. That puts roughly 17 hr 24 min of driving on the Los Angeles side and 14 hr 39 min on the Minneapolis 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. Denver still makes a fair, central place for Los Angeles and Minneapolis to converge, splitting the travel instead of asking one side to cross the country.
If Denver doesn't have what you're after, Albuquerque and Salt Lake City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Los Angeles and Minneapolis.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.