The fair place to meet is Kansas City, MO — the city closest to the midpoint of Buffalo and Tucson. From the farther side that’s about 21 hr 40 min of driving.
Recommended midpoint
Kansas City, MO
From Buffalo
17 hr 59 min
858 mi to Kansas City
From Tucson
21 hr 40 min
1,034 mi to Kansas City
Buffalo has the shorter trip; the split is off by about 3 hr 41 min. The alternatives below can even it out. Buffalo and Tucson are about 1,892 miles apart.
Buffalo and Tucson are about 1,892 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 17 hr 59 min of driving on the Buffalo side and 21 hr 40 min on the Tucson 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 Buffalo and Tucson 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 Buffalo and Tucson.
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 →
Buffalo is a city in the U.S. state of New York. It lies in Western New York on the eastern shore of Lake Erie and at the head of the Niagara River on the Canada–United States border. Read more →
Tucson is the county seat of and the most populated city in Pima County, Arizona, 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.