Another option is to ask at churches. Liability issues have made churches more squeamish, but the pastor may allow you to camp out back and use the facilities.
The most widespread free camping is on federal lands. You can camp for free on almost all Forest Service and BLM land - but you need to know where it is. Most is in the West - but there are national forests all over the U.S. This does NOT apply to National Park and National Wildlife Refuge lands - where random camping is prohibited. Most states lease state lands to ranchers or other users so random camping is not allowed. Some states DO allow camping at fishing access sites and on state game lands. Finally, don't random camp on Indian Reservation lands.
That is some pretty interesting information. It should be added as a sticky note.
I have biked several times in the US and never really done any wild camping, all because of the fear of meeting an angry redneck/farmer with a shotgun in the middle of the night with a couple of aggressive dogs. Everywhere you see the "No trespassing - Violators will be prosecuted" notes on tree trunks etc. Thus, I have been very cautious and reluctant in that matter. Maybe it is just an overreaction? Maybe I have seen too many movies? .
And like the thread starter: I find it absolutely horrible to pay 30 dollars for a tent site arriving at 8pm and leaving at 6am. All because the campground only operates with one fee = "Full RV hookup incl pull through for your convenience".
I'm interested in the church options. When arriving in a small sub-1000 town how do I establish contact with the pastor to ask for permission? Is this only possible when arriving early (=late afternoon) because he is around or at work? What if you arrive just before sunset? What is good practice and common sense in that matter?