A good choice for base camping for Yellowstone would be Grizzly RV Park in West Yellowstone. Nice clean CG with room for the larger rigs, FHUs, etc., and considering CG prices in the area, not terribly expensive. We have stayed there multiple times. Very convenient. If you don't have a toad, you may be able to rent a car in West Yellowstone for touring the park - much better than doing so in the 43' RV, though the latter is done all the time as well. Definitely plan several nights there. Get reservations for Yellowstone NOW.
Cowboy RV gets better ratings, but we have been to the Pocatello KOA several times & prefer the location - a little easier on/off from I-15, IMO, and though the park itself is old & a bit shabby, the scenery is better there than at Cowboy. For an overnight, it's fine, and has more sites available than Cowboy (from recent observation.
I second the above recommendation for the SLC KOA. For an urban CG, which it is, it has a surprisingly isolated feel, and many sites have some shade (a bonus in the summer!) I'd recommend asking for one of the premium sites if you're spending more than a night - they do have more space and are probably better for the longer rigs as well. They'll be closer to the facilities in the satellite building, which we found to be somewhat cleaner than those in the main building, due to the latter's proximity to the pool. Convenient to the downtown sites too (Temple Square, etc.)
2020 Toyota Tundra CrewMax 5.7L V8 w/ tow pkg, Equal-i-zer
2020 Lance 2375