Phoenix and Tucson are about 106 miles apart by road. Split the difference and you arrive near El Paso, the city closest to the halfway point between them. That puts roughly 7 hr 15 min of driving on the Phoenix side and 5 hr 33 min on the Tucson side — the fairest single meeting point among the cities near the middle.
At this range, El Paso works for a same-day meetup: close enough from both Phoenix and Tucson to meet for lunch or an afternoon and still be home by evening.
If El Paso doesn't have what you're after, Las Vegas and Albuquerque are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Phoenix and Tucson.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.