Since you'll be tent camping,finding available campsites shouldn't be a problem at all. You'll have to stick with public campgrounds most of the time but KOAs, Jellystones and private campgrounds around national parks do have tent sites. The US Campsite that Eycom posted is a very good site for public campgrounds.
Visit as many national parks as possible. Travel on the secondary roads when you can. It will really slow you down but you'll see so much more of the real country instead of just blacktop and other cars. Check out
Roadside America for the kitschy stuff. You can make a map marked with all of the places that you want to see along your route.
Have fun! It sounds like a great trip!