If you are in USA following information and site would be helpful!
From the looks of the Amtrak site, you'll have a variety of routes to choose from.
Amtrak
I was surprised to see that it's quicker to take the Empire Builder to Chicago and transfer to the City of New Orleans than it is to take the Coast Starlight to LA and then get on the Sunset Limited.
Amtrak usually offers pretty good service; it's certainly more relaxed than flying. Keep in mind that sleeping car accommodation prices include all meals in the dining car. For just an over night trip, you could consider booking just a seat as the seats are certainly spacious enough to sleep in overnight.
I think the circle route to New Orleans would be great: Empire Builder to Chicago and then City of New Orleans to New orleans on the way out; Sunset Limited to LA and then the Coast Starlight to Salem for the return.
Enjoy.