Fly into Salt Lake City and see Utah. Fly into Las Vegas and do Lake Mead, Hoover, St George, Valley of the Fire State Park, Zion, Bryce, Coral Sands, Monument Valley, Arches, Moab, Canyons and the North Rim and Antelope Canyon. You wont regret it.
The plan is to fly into Las Vegas, the onto Hoover, Grand Canyon for a couple of days (including a hike down & back in a day), then Sedona / Meteor Crater, Petrified forest, Four corners, Gooseneck Park, Monument Valley, Lake Powel, Kanab, Bryce Canyon, Zion Park, Mountain Meadows, St George.
Fly to SLC then attack the Northern part of Utah, plus Dinosaur Park, hopefully Hill Aerospace Museum - possibly including going to Moab (might try to squeeze it into the southern part of the trip!.
So we are doing virtually the State.
We have about 3 full weeks, plus a few days there.