I was always able to get into a hiker-biker campsites on the PCBR. I believe there was a three day limit for use which should be enough time to see the local attractions. I only stayed overnights, and kept going the next morning because it was such a great ride. You might want to try hostels or motels in or near large cities.
I have read there are some homeless persons who bike from campsite to campsite, stay their limit, and leave. I met one such person in a H-B site in southern California. He was very clearly not a cycling tourist, just a hobo or bum. One look at his bike and general demeanor said all that needed to be said on that matter. That's the way it goes sometimes. He did not bother anyone. However, I did see some more respectable, upright people filthing the H-B camping area by having their pet dogs deposit their waste there.
The PCBR is a tough, but also a very great ride. It is Americana writ large. I believe American society in general is somehow diminished by not having done it by bicycle. It would cause a general, overall improvement in American society if everyone could do it who were able. But of course I know it will never be, so it is left to us, the small minority, to pass the word along to others. Some will do it and others will stay home.
If you can cycle the PCBR at least once in your life---By ALL MEANS DO IT!