Denver and Phoenix are about 586 miles apart by road. Split the difference and you arrive near Albuquerque, the city closest to the halfway point between them. That splits the trip almost evenly — about 7 hr 1 min from Denver and 6 hr 55 min from Phoenix.
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, Tucson and Salt Lake City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Denver and Phoenix.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.