Detroit and Los Angeles are about 1,979 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 19 hr 4 min of driving on the Detroit side and 24 hr 43 min on the Los Angeles 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. Oklahoma City still makes a fair, central place for Detroit and Los Angeles to converge, splitting the travel instead of asking one side to cross the country.
If Oklahoma City doesn't have what you're after, Denver and Omaha are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Detroit and Los Angeles.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.