There is potable water at Lion’s Park in the center of Moab, and I believe at the Maverick gas station on the south end. I don’t think there is water at this campground or any other BLM campground in the area.

Shell and Maverick gas stations just south of Moab city center offer potable water (Maverick has free sewer dump stations too). Also, Gear Heads offers free water inside the back door of the store and Lion Park along River Rd has two free faucets in the lower parking lot. Could be other spots; but these seem to be the most popular and convenient in Moab proper

The Arches National Park Visitor Center has a water filling station right out front. During our Ken's Lake stay, we just filled up our water jugs there before heading back to the campsite.