For national forests check out this site. We used it all the time for finding our campgrounds with our 40' motorhome. There are definitely many national forest campgrounds that offer excellent site spacing and many are on trout streams, lakes or nearby. The couple who created this site have stayed in the campgrounds. They describe them clearly as to road access, facilities and what size RV would fit.
https://www.forestcamping.com/dow/pictures/pictures.htmTraveling in the western states it very easy to find sites as you prefer. There is lots of BLM lands and national forest lands. That's where you should concentrate for your desires. Next in line would be national and state parks. There are also excellent city and county parks. Forget about private parks. That's not what you want.
