One place you might consider, if you can get a site, is Dead Horse Point SP. It's a ways out of town, and very close to Canyonlands NP; not terribly far from Arches either. Fantastic place. The CG does have electric hookups, but no shade. A trailer your size should be able to fit at least several of the sites.
We did not have the same experience Lauren did at Spanish Trail, and we found it a decent place for us to stay. If you check with them, do ask for a site toward the back of the park, rather than the row near the road; it will make a difference in traffic noise at your site.
2020 Toyota Tundra CrewMax 5.7L V8 w/ tow pkg, Equal-i-zer
2020 Lance 2375