We love staying in the national parks for the best overall experience. You don't have to drive daily from the outskirts, you can enjoy the early morning and evening hours without the daytime crowds. For Grand Canyon - South Rim, try for Trailer Village in the park. It has full hookups and the free shuttle stops at the campground. You can ride all day long getting on and off wherever.
For Bryce the campsites are dry camping - no hookups. If you want hookups, Ruby's RV just outside the park is the best.
Zion - Watchman campground in the park has electric and dump station/water fill. The town of Springdale just outside the park entrance would be a good place to stay, too. Again, the free park shuttle stops in town.
Yellowstone - there are plenty of campgrounds in the park or outside the park at West Yellowstone, Gardiner or Cody.
If you go to Yellowstone, don't pass up Grand Teton Nat'l Park. It's a beauty and altogether different than Yellowstone. Gros Ventre campground or Colter Bay campground each have 300 dry camping sites and no reservations are accepted. We've always gotten a site, especially if you pull in during the morning. There's also Colter Bay RV which is right next to Colter Bay campground. The RV park has full hookups.
Have a good trip!
Full-Timed for 16 Years
.... Back in S&B Again
Traveled 8 yr in a 40' 2004 Newmar Dutch Star Motorhome
& 8 yr in a 33' Travel Supreme 5th Wheel