The fair place to meet is Las Vegas, NV — the city closest to the midpoint of Boise and Phoenix. From the farther side that’s about 10 hr 51 min of driving.
Recommended midpoint
Las Vegas, NV
From Boise
10 hr 51 min
517 mi to Las Vegas
From Phoenix
5 hr 22 min
256 mi to Las Vegas
Phoenix has the shorter trip; the split is off by about 5 hr 29 min. The alternatives below can even it out. Boise and Phoenix are about 737 miles apart.
Boise and Phoenix are about 737 miles apart by road. Split the difference and you arrive near Las Vegas, the city closest to the halfway point between them. That puts roughly 10 hr 51 min of driving on the Boise side and 5 hr 22 min on the Phoenix side — the fairest single meeting point among the cities near the middle.
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, Salt Lake City and Los Angeles are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Boise and Phoenix.
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 →
Boise is the capital and most populous city in the U.S. state of Idaho. It is the county seat of Ada County. The population of the city was 235,685 at the 2020 census. Read more →
Phoenix is the capital and most populous city of the U.S. state of Arizona. With over 1.6 million residents at the 2020 census, Phoenix is the fifth-most populous city in the United States and the most populous state capital. 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.