I've read other topics about Amtrak, and it seems to me like a decent way of travelling.
Maybe after several days in Chicago I would like to see another US city, going there by train.
Does anybody has travelled an Amtrak route from Chicago, either to New Orleans or to Seattle? Which one would you prefer, are there any stops on the way?
Any other advice/experience?
Each Amtrak route has its advantages depending on the season you plan to travel. There is a wealth of information on a rail fan website, trainweb.com
Check out the travelogues and station information.
I haven't done Chicago to New Orleans or Seattle, but I used to travel all the time out to SW Kansas when I was in school from the same line that goes from Chicago all the way out to Los Angeles. I still ride on the same line from time to time, and have always really enjoyed it. A good friend of mine worked on the line from Chicago to Seattle when we were in school, and he loved his job. I don't know that this helps you any in your travels, but it's good to know that the people on that line at least enjoy their work.