The fair place to meet is Kansas City, MO — the city closest to the midpoint of Las Vegas and Washington. From the farther side that’s about 23 hr 55 min of driving.
Recommended midpoint
Kansas City, MO
From Las Vegas
23 hr 55 min
1,141 mi to Kansas City
From Washington
19 hr 43 min
941 mi to Kansas City
Washington has the shorter trip; the split is off by about 4 hr 12 min. The alternatives below can even it out. Las Vegas and Washington are about 2,081 miles apart.
Las Vegas and Washington are about 2,081 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 23 hr 55 min of driving on the Las Vegas side and 19 hr 43 min on the Washington 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 Las Vegas and Washington to converge, splitting the travel instead of asking one side to cross the country.
If Kansas City doesn't have what you're after, Oklahoma City and Omaha are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Las Vegas and Washington.
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 →
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 →
Washington, D.C., officially the District of Columbia and commonly known as simply Washington or D.C., is the capital city and federal district of the United States. 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.