Live in the woods at a camp site.
Want to escape from the rut of work/bills/schedules and see the world? Try camping as a lifestyle. Every day is yours to do exactly as you please, you can travel, work seasonally, and rack up several lifetimes-worth of experience. Once you've tasted that kind of freedom it will be difficult to go back to a 9 to 5 existence.
Pick your mode of transportation. You're not going to want to sit around somewhere. Boredom is actually the toughest thing you'll face.
Hiking. Hiking is by far the hardest way to go. Everything you need is latched to your back, and the ground you can cover is limited. However, thousands of people hike incredible distances every year on major national scenic trails, and many find the experience addictive. Keep in mind that just because you're hiking doesn't mean you always have to be 'on the move'. Find a spot you like way off trail and stay as long as your food lasts. You can also use buses, cabs and shuttles to drop you off in the middle of nowhere, then hike in and find some place gorgeous to stay for a while.
Biking. Biking allows you to cover much greater distances, and it's easier than backpacking. However, you are tied to roads, instead of on trails. Get 'touring' bikes and rig them out with saddlebags and pull a cargo trailer. Mountain bikes can work also, if you plan on doing any off-road touring, or just exploring down trails and 4x4 roads. Bike touring is hardest in the mountains, with continual climbs. But the mountains are where the majority of public lands are in America, with lots of free camping. But if you have children, as well as all your gear, biking might not provide enough long-term room for you.
Canoeing. Get a 17'4" or longer for touring so it tracks straight. Camp on islands. You can swim, fish, and bathe every day. You can travel almost anywhere via big rivers, lakes, and canals. Water is where all the life is - you can guarantee every minute will be scenic. It's where towns are also, so getting groceries and necessities will be as close as the next bridge.
Get a 4 wheel drive vehicle and do them all. Use backpacking gear, put bikes on the back, and your canoe on top. This way you're ready for anything. You can leave the car and hike in, take a trip down a river, go explore an area on mountain bikes. If you have more than one bike, place rags between them so metal isn't scraped away going down bumpy 4x4 roads. Lightweight bulky items can be strapped in under the canoe. And the inside of a vehicle has all the room you'll ever need. The drawback of course is the cost of gas and repairs. But if you budget for it, and stay put in each spot as long as possible, you can make it work.