In 2011 I did this trip (below) over memorial day into June. I took 17.5 days driveway to driveway. I hit Rocky Mtn National Park, Moab, Arches National Park, Zion National Park, Bryce Canyon National Park, North Rim of the Grand Canyon, Monument Valley, Four Corners, and Mesa Verde National Park, along with several state parks along the way. It was fantastic. While in Utah I took time to explore some ghost towns, and some old washed away mining towns.
This book helped me plan a lot of it. See if you can find one on eBay cheaper as it's out of print now. I took most of my own food and extra water and fuel. Didn't have to use any of them but I came close with the fuel a few times.
One thing I was surprised about was the lack of fuel grade choices out west. Many places I stopped only had one unleaded option. Stop at your local BLM office once you get out there and they'll give you a map of all of their lands. Some will out line offroad trails for you. I wanted to drive to the Alston Point overlook and the Ranger highlighted the entire route for me. You can camp virtually anywhere on BLM lands. While you may be handy with a wrench, chances are you won't have cell service if something worse happens, so extra food and water - especially if soloing.
