It sounds like you're set for the Grand Canyon. Enjoy.
So for Zion, if you can, stay inside at Watchman Campground - electric, dump station and water fill. If you want a full hookup place, stay just outside the Zion entrance in Springdale. The free shuttle has a few stops in Springdale.
For Bryce, if you want hookups, Ruby's is your best bet - just outside the Bryce Gate. It has restaurants, fuel, laundry and a huge gift shop.
Flagstaff: if you have time drive the loop drive through Sunset Crater, just north of Flagstaff off Hwy 89. There are some neat Indian ruins along the drive.
Personally, if you're short on time with your stay in Flagstaff, I would skip Meteor Crater, Petrified forest and Painted desert. Instead, check out Walnut Canyon and the ruins.
Have a great trip!
