If I only had a dollar for every time this sort of post shows up on a backpacking forum, I could fund one of you guys with a dream and some wanderlust!

It's natural to want to go and explore, I think. What is not immediately apparent to you is the scope of what you are proposing.

You think it's going to be some romantic wonderful adventure. Somewhere around the time you're fined for being somewhere too long, or thrown out of the park, or are patching up your blistered feet for the 18th time, it'll set in that walking paved roads is hell on the feet, and home isn't such a bad place to be. Or about 1 am when you're wandering around looking for a place to stay, and all the good nooks and crannies are taken... the hotels and motels are full, so are the campgrounds, the hostels and the front step of the Y...

The suggestion has been made before to just get a cheap vehicle, throw in camping gear, and make that a mobile base of operations. That's probably going to be the best option for roaming the US, particularly if you are thinking of heading west into those states where it can be more than 100 miles of road without so much as a gas station - no water sources, no public lands, no campgrounds, no shade... Not safe for walking or hitchhiking.

You should rethink the hitchhiking. I don't know of a major highway in my state where it's legal. Would not surprise me in the least if the majority of the interstates forbid it, and in some states that's the only route to take.

If I were in your shoes, I'd go to Europe, where trains and public transit will get you everywhere. The US is just not conducive to that sort of backpacking.