Just to add to what others have said, here in the West, it's common for campgrounds to charge $10 for use of their dump station if you aren't staying there. You could generally fill up with fresh water there as well, though as already posted, be a bit wary of doing so. At a minimum, use a wet wipe or a weak solution of water and bleach to clean the exterior and interior of the hose that can reach.
Even the NFS campgrounds we've been to have water, but they often use spigots without hose threads, so you need something called a Water Thief to connect it to your fresh water hose and fill up your tank. Usually, those that don't have water make it pretty clear on their website that they don't.
When we recently stayed at Kings Canyon National Park, the campground there had no water or dump station of any kind. They said nothing of this on their website (or if they did, it evaded us). After carefully looking, we found a water spigot on the side of a restroom building and filled up there.