Albuquerque and Dallas are about 587 miles apart by road. Split the difference and you arrive near Oklahoma City, the city closest to the halfway point between them. That puts roughly 10 hr 49 min of driving on the Albuquerque side and 4 hr on the Dallas side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Oklahoma City suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Oklahoma City doesn't have what you're after, El Paso and Austin are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Albuquerque and Dallas.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.