Below is a partial list of some of the options for you and your family, but keep in mind, I am flexible to what you want! 
 LocationNumber of Days*  Things to see and do
  Great Basin National Park 1-3See the world's oldest living things (Bristlecone Pines), Nevada's only glacier, and the world-class Lehman Cave. 
 Capitol Reef National Park 2-4
Take in the world's best example of a monocline in Capital Reef.
 Bryce Canyon/Zion National Park2-4View the monolithic sandstone cliffs and high country of Zion and the narrows of the Virgin River and hike amongst the brilliant mudstone hoodoos of Bryce Canyon.
 Arches/Canyonlands National Park/Moab 2-4Look at the delicate spans of Arches before they fall and gaze at the endless spires and grooves of Canyonlands, including Upheaval Dome, an ancient meteor crater!
 Grand Canyon National Park 2-4Experience Grand Canyon, one of nature's greatest wonders.  

 Yellowstone and Grand Teton National Parks2-4 Explore the world's first national park, with all of its geothermal features, including geysers, hot pots, and the great wildlife and views.
 Glacier National Park 3-5Visit the frozen north of Montana and drive the famous "Going to the Sun" road of Glacier.
 Yosemite/Sequoia National Park 3-5 Scale the famous Sierra Nevada mountains and see Yosemite Valley, Kings Canyon, and the largest trees on earth, the Sequoia Redwoods.
 Rocky Mountain/Black Canyon National Parks/Colorado 3-5
Revel in the high alpine snow and deep canyons of Rocky Mountain/Black Canyon.
Crater Lake National Park/Oregon 3-5 
Observe one of the most beautiful places in the world in America's deepest and purest lake: Crater Lake, formed within a volcanic caldera.
 Southwest South Dakota4-7 Road trip to the array of fabulous sites southwestern South Dakota and northwestern Wyoming can offer, including the Badlands, Mount Rushmore, Devils Tower, Wind Cave, and Jewel Cave.
 Carlsbad Caverns/Guadalupe Mountains National Parks4-7

Trek the famous Carlsbad Caverns of Eastern New Mexico and the Guadalupe Mountains of West Texas. 
 Glacier/Yellowstone4-7 See Glacier and Yellowstone in one big loop.
 Grand Staircase4-8 Combine the Bryce, Zion, and Grand Canyon trips.
 Grand Circle6-12  Combines Great Basin, Bryce, Zion, Capitol Reef, Grand Canyon, Arches, and Canyonlands.
*Schedule is adjustable to your specific wants and needs. A "day" includes travel from Salt Lake City, unless another arrangement is made. Nights spent on trip are one less than the day count.