Sounds like you can do w/o hookups. If you want to be in the park, you might consider Bridge Bay, Grant Village, Madison, Mammoth or perhaps Canyon CGs. You WILL need reservations, and will need to ask if your rig will fit in your site - some sites will be long enough, but others won't.
If you want hookups, to be inside the park you have one option: Fishing Bridge RV Park. Again, you will need reservations. Outside the park, IMO the best and most convenient CG is Grizzly RV Park in West Yellowstone - only a few blocks outside the west gate of the park, nice & tidy, etc., and full hookups.
Most of the CGs inside Yellowstone allow generators (be sure to ask about the one you choose) but there are restricted hours, just FYI.
2020 Toyota Tundra CrewMax 5.7L V8 w/ tow pkg, Equal-i-zer
2020 Lance 2375