I would recommend both these parks for overnight or short stays - depends on what you look for in a park.
Snowville, UT, the Lottie-Dell. Easy to get to, honor system for paying, gravel sites with grass and picnic tables, no fancy amenities, good scenery.
Vernal, UT, Fossil Valley RV. Right on highway 40, sites have grass, mature trees and picnic tables. Here again, mainly honor system, no fancy amenities. There is a Smith's grocery and fuel station and a Golden Corral across the street. We stayed there a week but didn't need a pool or recreation area - it was HOT, and we worked outside during the day, so we were too tired when we returned to the Montana to care about much of anything except the air conditioning!