It will be a great trip!
Badlands: Of course Mt Rushmore, Sturgis motorcycle museum even if you are not a bike owner (we're not) it's worth it. Deadwood: have a drink in the saloon where Wild Bill Hickok was assassinated and Mt Moriah cemetery, his grave and Calamity Jane's. Drive through Badlands National Park and Custer State Park. Drive the Needle's Hwy. If it interest's you, drive a little east of Rapid city and visit a Minute Man Missile silo.
We stayed at Beaver Lake Campground just outside Custer, but there are many to choose from. There was a western spring rally at a campground near Hermosa last year, maybe someone here can recall the name, we didn't attend so I can't recall.
Glacier: If you are there in June, most likely the GTTSR won't be open yet but you can ride your bicycles or e-bikes on it up until the avalanche closures from each side. Early June we were able to ride the entire road except a short stretch of it at Logan pass, it was amazing. If the road is open, Dually's are over dimension for it and the best way to see it is in a Red Bus. Let the experts drive. Expect big crowds, parking was hard to find on the west side because people come from all over the country to bike it. Hit it early. If you are there around July 1st, the road may be open by then. You can get info on road clearing progress and how far they have progressed on their web site. We stayed in West Glacier at the KOA.
Yellowstone: Stay in the park at Fishing Bridge. You really don't want to wait in line everyday to get in the gates, and it enables you to get out early. We spent 5 days, could have used more. Hit all of the highlights, and try to get to the Lamar Valley early to possibly see wolves. Go after Memorial day to increase the chance that The Beartooth Hwy will be open, it's worth it. If you get a rain day, use it to visit the Buffalo Bill Cody Museum in Cody. I could spend 2-3 days just in there. The firearms museum part of it had us for hours. We stayed at Fishing Bridge.
Tetons: We stayed at Gros Ventre campground and day tripped to Jackson and the Tetons from there.
Canyon Lands and Arches: We split time between Dead Horse State park Wingate campground and Spanish Trails RV park in Moab. Hike Arches, go to Dead Horse point at the state park. Rent a jeep or SxS or sign up for a Jeep Safari.
Bryce: The sites from the rim are great but hike some of the trails if you can. I saw all the pictures, but walking up to the rim for the first time and seeing the hoodoos was mind blowing. We stayed at Ruby's.
Zion: Beautiful, but again, it's a hikers paradise. We stayed in the park at Watchman Campground. We could walk across the pedestrian bridge over the river and into town for restaurants and events etc. If you can't get into watchman, you need to get there real early to get a parking spot. Drive Rt 9 east from Springdale through the tunnel (without your rig) and hike the Pine Creek Canyon overlook trail. The payday at the end of the trail is being above the canyon overlooking the switchbacks in the road you drove up there on.
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It's been several years since we were at Grand Canyon, things may be different and I may not remember things right so I'll pass on that one. Have Fun and be safe.