Amtrak does the train equivalent of a cruise liner, where you spend about half a month on a sleeper car travelling all over America. It's cheaper than an actual cruise line, and more importantly I think trains are cool.
Edit: forgot about the unlimited money. I guess I would pay to replace all the rails in north america first so I have a smooth ride the whole time.
I'm assuming you're talking about the All American, as that's the main one I could find. About fifteen days, and $2400. Which is about as much as a three to five day cruise, depending on cruiseline.
That sounds awesome, and isn't that terribly expensive, honestly. My wife and I went on a similar route road trip for our honeymoon a few years ago and it was in that same ballpark of cost, between car rental, hotels, and other expenses.
It looks like you'll still be needing to pay for hotels for the nights you aren't traveling. Still, not bad especially since you don't have to deal with the hassle of driving. You just get on the train, sleep, and just appear at the next location.