National Park: Zion
Alternative: Coral Pink Sand Dunes State Park
Southeast of Zion National Park, on the border between Utah and Arizona, lies a 265-acre "shifting sea of red sand" flanked by Navajo sandstone cliffs. You can camp, you can ride dune buggies, and you can probably do that sand snowboarding thing you sometimes see in commercials, all for six bucks.
In the neighborhood: You're only an hour-and-a-half drive away from Lake Powell, the "second-largest manmade reservoir" in America (on the Colorado River), and first-largest one named after a one-armed Civil War vet.