Take Route 66 where you can for a slice of automotive history, Grand Canyon (must see), Santa Fe NM (cool). Austin TX still has a great music scene. Take lots of pictures.
When you get to New Orleans you could retrace the route the Top Gear crew used through the deep south into Florida... maybe paint "Hillary for President" and "Nascar Sucks" on your car for added excitement. It worked pretty well for those guys.
It should be a great trip. I have been as far as Houston several times but never into Louisiana. Enjoy!