The fair place to meet is Las Vegas, NV — the city closest to the midpoint of Salt Lake City and Tucson. From the farther side that’s about 7 hr 36 min of driving.
Recommended midpoint
Las Vegas, NV
From Salt Lake City
7 hr 36 min
363 mi to Las Vegas
From Tucson
7 hr 35 min
362 mi to Las Vegas
That’s an even split — both sides drive within 1 min of each other. Salt Lake City and Tucson are about 592 miles apart.
Salt Lake City and Tucson are about 592 miles apart by road. Split the difference and you arrive near Las Vegas, the city closest to the halfway point between them. That splits the trip almost evenly — about 7 hr 36 min from Salt Lake City and 7 hr 35 min from Tucson.
That's a half-day drive from each side, so Las Vegas suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Las Vegas doesn't have what you're after, Phoenix and Albuquerque are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Salt Lake City and Tucson.
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 →
Salt Lake City, often shortened to Salt Lake or SLC, is the capital and most populous city of the U.S. state of Utah. It is the county seat of Salt Lake County, the most populous county in the state. 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.