As for an average price, I would say on average, you'll looking at $20.00. In Florida I paid close to $30.00 a few times, and in New Mexico and parts of west Texas, paid about $9.00. When you look over the ACA maps, you'll notice that the majority of the referenced campsites are privately owned, or at least a smaller variety state/county park. All of the private parks are more than familiar with cyclists coming through, some going so far as to have cyclist as part of their business model (separate, well kept, flat, grassy areas...) It goes without saying that you're not going to require the standard RV hookups, etc, so a plot of land for a tent is easy to accommodate. Either way, most of the camping services referenced are well priced.
Arizona, especially just east of the CA border, has plenty of places where you can camp out with no trouble (pull off on the side of the road, etc...) Eastern CA is much the same (Octillo for example...)
Enjoy the trek, it's unbelievably amazing