I've done a smaller version of that ride - Durango to Death Valley. Depending on which route you take, you could stop at a variety of parks, etc. Zion and Bryce are the two to not miss, but they might be a bit of a detour. Death Valley is also cool, as is the canyon just beyond it - maybe called Black Canyon....?
Plan for a little extra time. And remember that the gas stations in Nevada and eastern Cali are farther apart.
If you don't have a place to stay yet, the little casinos on the border of Nevada and Cali are cheap and interesting. The one I stayed at years ago had Bonnie and Clyde's Ford, all full of bullllet holes. They had his shirt too, also full of bullet holes - weird display.
Good luck on the ride!
