Grutas de Garcia is Monterrey's classic cave excursion, set in the dry hills west of the city. The chambers are big, theatrical, and full of the limestone formations you want from a show cave, with the added oddity of marine fossils in rock now lifted far above sea level.
The approach is part of the day. A cable car sometimes handles the climb to the cave entrance, but you should check its status because walking up is possible and tiring. Either way, the caves justify the trip if you want a natural sight beyond the urban mountain viewpoints.