The fair place to meet is Kansas City, MO — the city closest to the midpoint of Cleveland and Las Vegas. From the farther side that’s about 23 hr 55 min of driving.
Recommended midpoint
Kansas City, MO
From Cleveland
14 hr 38 min
698 mi to Kansas City
From Las Vegas
23 hr 55 min
1,141 mi to Kansas City
Cleveland has the shorter trip; the split is off by about 9 hr 17 min. The alternatives below can even it out. Cleveland and Las Vegas are about 1,825 miles apart.
Cleveland and Las Vegas are about 1,825 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 14 hr 38 min of driving on the Cleveland side and 23 hr 55 min on the Las Vegas 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. Kansas City still makes a fair, central place for Cleveland and Las Vegas to converge, splitting the travel instead of asking one side to cross the country.
If Kansas City doesn't have what you're after, Omaha and Oklahoma City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Cleveland and Las Vegas.
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 →
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 →
Las Vegas, colloquially shortened to Vegas, is the most populous city in the U.S. state of Nevada and the county seat of Clark County. It is the 24th-most populous city in the United States, with 641,903 residents at the 2020 census. 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.