Camp free in National Forests
Almost all National Forests allow free dispersed camping. Just call the national park before you go to make sure, and ask if they have any fire restrictions at the time (don't start a campfire in dispersed camping if they have restrictions). See here for rules:
They don't have "campsites" with picnic tables, toilets of any kind, running water, fire rings, or anything–just you in the middle of nowhere off a forest service road (look up minimum distance you should have your tent from the road. We love the adventure of truly roughing it. We got a garage sale folding camp table, made our own portable toilet out of a potty training seat and a corugated plastic sign (like the ones on telephone poles that shouldn't really be there), and bring our own water, and it's great. We actually prefer this to campgrounds since we can't hear or see any other people, and our young children making noise at night don't bother anyone.
Last summer, we spent a week vacation staying at a different national forest each night, all for free, and just called each day to the one we thought we'd end up at that night. Many national parks have national forests right next to or around them, so we would spend the day at a national park (got the annual pass) then camp for free in the national forest right by it.