Anchorage and Tucson are about 2,650 miles apart by road. Split the difference and you arrive near Portland, the city closest to the halfway point between them. That puts roughly 32 hr 17 min of driving on the Anchorage side and 23 hr 18 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. Portland still makes a fair, central place for Anchorage and Tucson to converge, splitting the travel instead of asking one side to cross the country.
If Portland doesn't have what you're after, Seattle and Sacramento are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Anchorage and Tucson.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.