For fresh water, we just filled our 6 gallon jugs at White City, from a kiosk, I think it was $1.25 per jug. That's the closest for any water, I know of no "hose friendly" place to fill. But we really enjoyed our stay.
We liked Chosa for it's central location to the Caverns
White City will be the closest. Not sure what the charge would be. We camped there for one night to dump and fill. Carlsbad has a Pilot/Flying J. But, when we were there, the outside faucet was broken and we couldn’t even get fresh water.