You might check, but National Forest areas typically also permit dispersed camping -- away from established sites. We've had some of our best camping experiences heading down fire roads and off into the bush a bit. No neighbors, no noise. We dry camped at one off Minarets Road in the Sierra. We saw not a single person over two days, and had a sweeping view of the Sierra crest. It was a dry site, so we had to hunt down water, but it was great.

State parks -- at least in CA and OR -- often have hiker/biker sites that are available to whomever wishes to drop in (hikers and bikers only) and no reservations are required.