We were in Carlsbad, NM in May. We stayed at the Carlsbad RV Park - which I think was formerly KOA. We called on Friday and made reservations for Sunday-Monday. Most of the sites are occupied by the workers, but there were several available for short-term stays. Very nice park. It was several miles from the Caverns, but I think it was the better option as far as campgrounds were concerned.
At the Caverns, the elevators were working when we were there. Actually, an elevator technician rode it with us when we went down. Said they were working on another one.
If you happen to need a campsite near Albuquerque, we stayed at the Happy Trails RV Park in Moriarty, NM. They are new owners and are doing a great job to make it a great stop for us RVers. It is east of Albuquerque just off I-40. Happy Travels!!