A room can be booked for the longer train journeys, with a shower and tolet etc.. We had a room on the train from Flagstaff (near the Grand Canyon) to Chicago ( the train started at LA) last year, our journey took about 44 hours, but we got off on the way.
It can be a great way to see the country, as stations tend to be in the centre of town, they re handy to get to. Most of the longer routes have double decker trains witha site seeing lounges on the upper deck with seats pointing out to the scenery. If you book a room the meals in the dining car come as part of the price, and I found the food excellent ( 2 and three course meals, with steaks etc.).
I found it a very nice and relaxing way to travel, with less of the hassle involved with geting to airports on the edge of town etc. and security etc. Most of the stations were very nice and clean, and the staff very courteous. I cetainly plan more train trips in future.
One caveat, was that we had planned to get a train from Chicago to New Orleans before the disaster in NO, we chose to get off in Memphis instead and visit Graceland, the full dining service was cancelled on this route because of lack of custom, but the train was fine besides. You can book the rooms/tickets online, price wise they weren't that bad, and Amtrak were very easy to deal with when we needed to change our tickets.