While I have not stayed at any of these parks I am living nearby and have looked at them. As suggested the KOA seems to be the best choice and I believe that you will see several votes for it. There is also Brantley Lake State Park in the area if you are inclined.
One suggestion and one caution if I may.
The suggestion is to try to drive a little farther down the road and visit Guadalupe Mountains Nat Park if you have time. A stop at the visitors center and Frijole Ranch house would be a nice stop if you have never been in this area.
The caution is to be aware of the weather. I don't know where you are coming from or your schedule but the weather is being forecast to change significantly on Sat with forecasts of rain and snow with much colder temps. This area has a tendency to have freezing rain as well and the roads do get closed at times so just be informed.
The last thing that comes to mind is that some time back there was a report that the elevator into the caverns was out of service so the only way in and out was the walking entry. Don't know if this is still the case or if it is important to you but wanted to share.
Hope you have a great trip.
Terry
