Specifically
- National Parks will allow you to stay up to 14 days consecutively, at which point you must move on. BLM land, on the other hand, such as around Quartzsite, AZ can be done up to 9 months. An RV would be very, very useful here. You can boondock for free.
- Legal Nomads and Tim Ferris both recommend renting accomodation for a few months at a time, using Craigslist as a resource. This may optimize your tradeoff.
- Don't forget local parks and local churches. Many will allow travellers to stay for the night, and indeed the Trans-America Trail even has spots marked out.
- Local WalMarts and other big box stores will let you boondock for a night, maybe two. It's not a long-term thing, however.
If you need additional work, plus a place to stay
Many campsites need camphosts. Tey will let you stay in a place for free, in exchange for light duties around the site.
Many volunteer opportunities exist that will give you a place to stay. Church camps, Peace Corps, Teach for America - travel opportunities exist.
- Becoming a Truck Driver may give you the road freedom, a place to stay, and some income. That said, if your real source of income is IT, the schedules may be a bit too tight to accommodate.
- In cities, Homeless Shelters sometimes take in volunteers to stay the night with the residents. Local churches may do the same.
More generally
As to actually living the nomadic life, its something I keep dreaming about researching, and the overall consensus seems to be that an RV will let you do what you want in this regard. For the last several years, I've been following RV Dreams in particular, as the two people who run it post their daily experiences and their finances. Its not a trade-off free environment, but there seems to be much to recommend it.
Income on the Road is readily available - IT work is usually the best, although Workamping can earn you minimum wage and a place to stay, if you don't have other skills. Beyond that, there is a whole internet segment dedicated to Digital Nomads
Additionally, this book by some guy named 'Tynan' talks about easing into the nomadic lifestyle. He covers much of the same ground, saying an RV is your ticket to freedom. His book tends to be a bit more preachy on the exhortative side, but he covers the subject fairly well.
One major caveat - and this from a guy whose been struggling not to jump in for the last four years - it's a major lifestyle change. I'm 41, in the process of trying to get divorced but still take care of his kids, and oddly enough, financially stable enough to swing this. When my divorce is complete, I will have more than enough money to not work again. This is an amazingly tempting idea. But you know, the reality of leaving corporate America is scary in and of itself. If you're young, it might be perfect. If you're old, it might be exhilarating. And, from what I've read, it might even be doable :)
Just don't forget its every bit as much mental as it is physical and financial.