Albuquerque and Los Angeles are about 663 miles apart by road. Split the difference and you arrive near Phoenix, the city closest to the halfway point between them. That puts roughly 6 hr 55 min of driving on the Albuquerque side and 7 hr 29 min on the Los Angeles side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Phoenix suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Phoenix doesn't have what you're after, Tucson and Las Vegas are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Albuquerque and Los Angeles.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.