The only time you will need to have reservations is around the tourist areas. It shouldn't be a problem any place else. I hate being tied to a schedule when I am on vacation. That makes if more like work. It drives my wife crazy because she is always worried we won't find a place to stay. I travel 3-4 weeks every year and I have never had a problem finding a place to stay. I like staying flexible. Sometimes you will run into people that will tell you about some really interesting place they saw. I can alway change my plans to see those kind of places.
Here is a link to find free camping. http://freecampsites.net/usa/
You can generally camp anywhere on public land and that is usually free also.
Go on line to the states you want to travel and get their tourist guides. They are free and give good information.
Information you get from the states will also include camping.
It will be hot in some of those areas in June so be prepared.
You will have a great time.