Personally I really liked placed like Boulder, Death Valley, Grand Canyon and of course the mandatory Route 66 by car?
Other places I would like to visit is Washington. I would love to see the White House and check out the smithsonian institute!
It really depends on what you wish to see? If you are to roadtrip there are plenty of forums upon this - just a quick Google search shows this (sorry if not allowed!):
https://roadtripusa.com/ this website gives you various destinations to road trip. If you are to stay for longer periods of time I would really recommend Boulder? Beautiful nature, great trails and an amazing brewery.
Hope this helped?