Albuquerque and Denver are about 334 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 4 hr 49 min of driving on the Albuquerque side and 11 hr 41 min on the Denver side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so El Paso suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If El Paso doesn't have what you're after, Salt Lake City and Phoenix are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Albuquerque and Denver.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.