I did this alone for my winter break of freshman year of college. To the best of my recollection, my itinerary was Portland -> Vancouver (BC) -> Toronto -> New York -> New Orleans -> Ft Worth -> Joshua Tree -> LA -> SF -> Portland. One month. I arranged to either sleep on the train or crash with friends (knew someone in most of those places). The diner car was pretty expensive, so I generally carried a little food and ate heavy when I hit stopping cities. A significant portion of the 30 days was spent in a train, from what I recall.

Traveling by train has a special extra something; you're with the people you travel with for long enough to actually develop a conversation, but you're with them just short enough that you don't have to worry too much if you don't hit it off. This was great for an introvert like me to practice chatting up strangers with little risk in a safe setting. And you meet a really interesting mix of folks, different from the people I normally find myself talking to. It's particularly fun to feel the gradient of humanity / culture shift as you travel.

I traveled light; just a backpack, a camera, and a laptop (well, and climbing shoes for J-Tree). I was super careful about keeping the tech gear hidden and slept wrapped around my bag when I slept in public spaces (train stations / trains).

One thing about traveling by train: Amtrak is always late, and often by half a day. Make sure people who might be meeting you at connections know this and don't expect it to work like air travel.

Anyway, my thirty days of independent travel was a fantastic experience, and I'd really recommend it to anyone, young or old. You can even comfortably get work done in the passenger cars. Tether to your 3G phone or whatever and you're riding the Rails in style.