We went out west (from VA) and back a couple of years ago with our travel trailer and our family of six. Touched 21 states in 30 days and took in Ancient Puebloan Ruins, Las Vegas, San Diego, Grand Canyon, Yellowstone, Yosemite, and Mt. Rushmore to name the highlights.
Keep in mind that you can wing most of the trip with few reservations. However, the National Parks will require reservations waaay in advance. We sort of locked those in and worked around them.
So much beautiful country to see, so little time. Enjoy your adventure!