The fair place to meet is Albuquerque, NM — the city closest to the midpoint of Denver and Tucson. From the farther side that’s about 7 hr 1 min of driving.
Recommended midpoint
Albuquerque, NM
From Denver
7 hr 1 min
334 mi to Albuquerque
From Tucson
6 hr 40 min
318 mi to Albuquerque
Tucson has the shorter trip; the split is off by about 21 min. The alternatives below can even it out. Denver and Tucson are about 617 miles apart.
Denver and Tucson are about 617 miles apart by road. Split the difference and you arrive near Albuquerque, the city closest to the halfway point between them. That puts roughly 7 hr 1 min of driving on the Denver side and 6 hr 40 min on the Tucson side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Albuquerque suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Albuquerque doesn't have what you're after, Phoenix and El Paso are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Denver and Tucson.
Albuquerque is the most populous city in the U.S. state of New Mexico. Founded in 1706 as La Villa de Alburquerque by Santa Fe de Nuevo México governor Francisco Cuervo y Valdés, and named in honor of Francisco Fernández de la Cueva, 10th Duke of Alburquerque… Read more →
Denver is the capital and most populous city of the U.S. state of Colorado. Officially a consolidated city and county, it is located in the South Platte River valley on the western edge of the High Plains, and is just east of the Front Range of the Rocky… 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.