Albuquerque and Omaha are about 721 miles apart by road. Split the difference and you arrive near Denver, the city closest to the halfway point between them. That puts roughly 7 hr 1 min of driving on the Albuquerque side and 10 hr 13 min on the Omaha side — the fairest single meeting point among the cities near the middle.
That's a half-day drive from each side, so Denver suits an overnight or a weekend rather than a quick coffee — long enough to want a reason to stay, short enough to drive.
If Denver doesn't have what you're after, Oklahoma City and Kansas City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Albuquerque and Omaha.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.