Depends how long you have, obviously, but if you want to see the Grand Canyon, and nothing has ever taken my breath away like that, there are other National Parks, Bryce Canyon, Zion, and Canyon de Chelly, there's then Monument Valley in Utah and the Mesa Verde in Colorado, which is fabulous and further north, Arches NP in Utah. I think you would need 3 weeks to do all of these, there are some long distances involved, but designate "driving days".
You can also get down to Las Vegas and given time, further west into Yosemite NP.
A lot of the parks close entirely or in part from around November until even mid May, check on the National Parks website, it's very helpful.