The fair place to meet is Oklahoma City, OK — the city closest to the midpoint of Cleveland and Los Angeles. From the farther side that’s about 24 hr 43 min of driving.
Recommended midpoint
Oklahoma City, OK
From Cleveland
19 hr 55 min
950 mi to Oklahoma City
From Los Angeles
24 hr 43 min
1,178 mi to Oklahoma City
Cleveland has the shorter trip; the split is off by about 4 hr 48 min. The alternatives below can even it out. Cleveland and Los Angeles are about 2,045 miles apart.
Cleveland and Los Angeles are about 2,045 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 55 min of driving on the Cleveland 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 Cleveland 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 Kansas City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Cleveland and Los Angeles.
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 →
Cleveland is a city in the U.S. state of Ohio and the county seat of Cuyahoga County. Located along the southern shore of Lake Erie, it is situated across the lake from Ontario, Canada, and is approximately 60 miles west of the Ohio–Pennsylvania state line. Read more →
Los Angeles (LA) is the most populous city in the U.S. state of California, and the commercial, financial, and cultural center of Southern California. 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.