Cedar Pass Campground is 18 miles down the road inside the National Park. It has a dump station, garbage bin, and potable water. The sign says $1 but they told me at the entrance it is free and I used it with no problems.
We went to Frontier Cabins, travel North on 240 (towards Wall, SD). It was a few miles from Nomad View Dispersed. On the side of the check in building is a water spigot. We asked if we could fill our water bladder and they said it wasn’t a problem at all. Always talk to them first but they were very nice about it.