I'm thinking about Austin, Albuquerque, Santa Fe, and then San Diego...then back a different route.
When I moved from San Diego to the East Coast I took almost 2 weeks to drive across the country seeing all the "off the beaten path" tourist traps.
Old Tucson movie studios, OK Corral, Tombstone, Carlsbad, Roswell, Albequerque, Cadillac Ranch (just south of Amarillo); Hot Springs, Arkansas, etc...
Had a blast and I was by myself. Me, my car, a bike on a rack and a few changes of clothes. The Navy was moving me and they wouldn't have my stuff to the east coast for almost 3 weeks, so I just took my time.