The fair place to meet is Oklahoma City, OK — the city closest to the midpoint of Tucson and Washington. From the farther side that’s about 24 hr 6 min of driving.
Recommended midpoint
Oklahoma City, OK
From Tucson
16 hr 51 min
803 mi to Oklahoma City
From Washington
24 hr 6 min
1,149 mi to Oklahoma City
Tucson has the shorter trip; the split is off by about 7 hr 15 min. The alternatives below can even it out. Tucson and Washington are about 1,951 miles apart.
Tucson and Washington are about 1,951 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 16 hr 51 min of driving on the Tucson side and 24 hr 6 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. Oklahoma City still makes a fair, central place for Tucson and Washington to converge, splitting the travel instead of asking one side to cross the country.
If Oklahoma City doesn't have what you're after, Memphis and Kansas City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Tucson and Washington.
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 →
Tucson is the county seat of and the most populated city in Pima County, Arizona, United States. 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.