Do take as long as you can in Utah. We spent 3 weeks in the fall
of 2013 and visited 5 fabulous and distinctive National Parks; Zion, Bryce, Canyonlands, Capital Reef and Arches. If you are 62 or older and a US citizen you can buy a lifetime pass for $10, unbelievable! A year-long pass is usually $80 (still worth it). Our favorite campgrounds turned out to be BLM lands outside of Canyonlands (pit toilets, picnic tables, fire pits and water) and Capital Reef (no amenities). I also suggest that you use the "Search" button at the top of this page, scroll down to the Google Search and enter "Utah". You will find a TON of previous posts. Have a great time!
Note: Top and bottom photos are Zion and middle photo is Capital Reef.