Earlier quoted context omitted.
I recently toured for 5 months in the US on my bicycle. My average cost was $30 per day. That included sightseeing, an airline ticket every month and a bus ticket every month. I used Warm Showers and wild camping, so I rarely paid for housing. $7.25 per hour is enough to live on. You just need to work enough hours, do long commutes and be very, very disciplined in all your purchases.
Question for you: at most national/state parks, there are available campsites that cost in the range of $5-$20 per night. These are advertised on their usual websites. These are sites for car camping. However, the couple times I've called, I've asked about primitive camping (aka hike into the woods and camp at the primitive sites), and it turns out that this is free. But the primitive campsites aren't ever discussed…
AFAIK, primitive camping for a night or two in a National Forest is free. Just be far enough away from roads and water sources. And many national parks have national forests near them.
Also check out freecampsites.net
I did camp on private property a few times without permission and only got discovered once: It was at a church and the pastor gave me free breakfast.