Surprising few options in the area. There is one RV park at the turn off to the caverns. But you can check rvparkreviews.com and see it is not well thought of. There is a very nice KOA about 15 miles north of the town of Carlsbad. We stayed there once and would again. There is also an RV campground at Brantley Lake State Park that gets decent reviews, just a little south of the KOA. Have not stayed there.
If you are in relatively good condition I suggest walking in the natural entrance, tour all the self guided parts, and take the elevator back out. Don't try to walk out the natural entrance unless you are in very good physical condition. There are several guided tours off the main path you can sign up for. But I have not taken any of them.