Spend the most time in Yellowstone & the Tetons.
๐ What kind of camping rig do you have? That would be helpful info for those of us who want to help you with suggestions.
If you need hookups, your only choice inside Yellowstone is Fishing Bridge RV Park. Otherwise you will need to camp outside the park, or choose a no-hookups site. Mammoth CG (no hookups) is friendly to campers bigger than tents; Gardiner has a couple private CGs with hookups (we stayed at Rocky Mt RV Park there; it was decent & has some nice views). The road from Gardiner into the park, specifically involving the arch, is under major construction this year, though - just FYI.
IMO the best CG for the Tetons (with hookups) is Colter Bay RV Park. Lots of folks recommend Colter Bay CG (north end) or Gros Ventre CG (south end) for the Tetons - no hookups in either one.
Be aware that many CGs that take reservations will already be pretty booked up. Good luck!
2020 Toyota Tundra CrewMax 5.7L V8 w/ tow pkg, Equal-i-zer
2020 Lance 2375