The trip in short
Pick up the camper in Las Vegas, stock up, and drive into the parks. Three nights at Zion for the Narrows and Angels Landing, sunrise over Bryce Canyon, Capitol Reef on Scenic Byway 12, and three nights in Moab for Arches and Canyonlands. You camp facing the Mittens in Monument Valley, see Antelope Canyon and Lake Powell from Page, and end at the South Rim of the Grand Canyon. A campground among the rocks every night: the classic among the camper trips.