El Paso and Tucson are about 265 miles apart by road. Split the difference and you arrive near Phoenix, the city closest to the halfway point between them. That puts roughly 7 hr 15 min of driving on the El Paso side and 2 hr 39 min on the Tucson side — the fairest single meeting point among the cities near the middle.
At this range, Phoenix works for a same-day meetup: close enough from both El Paso and Tucson to meet for lunch or an afternoon and still be home by evening.
If Phoenix doesn't have what you're after, Albuquerque and Las Vegas are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between El Paso and Tucson.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.