It sounds like a great itinerary and I'm sure you will have a wonderful trip.
I'm British and have been living in the US for quite a few years. I'd like you to be aware from the outset that train travel is rather different here in the US.
The long distances mean that most trains are sleeper trains and come with a dining car, that you probably know. Prices are very reasonable compared to the UK if you ride coach class (without a sleeper). The fares for sleeper accommodation vary drastically depending on when you're travelling and when you book. If you can get one of the "low bucket" fares, it can be very good value indeed, especially when you consider all meals are included. However, the higher fares can be very expensive indeed. Check
http://amsnag.net/ to find out the lowest fares.
What you may not know is that American trains are very underfunded and this lack of funding causes some difficulties for the traveller. Outside the northeast corridor, the rail network is skeletal at best, and often non-existent (hence no service in Nashville). Moreover, most arrivals from Europe are surprised to learn that so few trains run between major cities. For example, Chicago and Memphis, two major cities within 10 hours' driving distance, are connected by only 1 train each way per day. Another surprise for me was that train stations are often inconveniently located in cities with no easy ground transportation to the central area. That being said, New York and Chicago both have their stations located fairly centrally and have very good public transportation systems. From New Orleans, you'll probably need to get a taxi for your destination if you're staying in the French Quarter. The Memphis station is quite central but downtown Memphis is not particularly exciting, other than touristy Beale Street, and you'll be arriving either late at night (if you come from New Orleans) or around dawn (if you come from Chicago). So you'll probably need to figure out plans for a taxi when you get to Memphis, and perhaps consider hiring a car for your stay there, particularly if you want to see Graceland, which is outside the city centre. For the other cities, you are probably better off without hiring a car.
If you're cutting out Nashville but want to add in another city that's easily accessible by train, I'd say the obvious choice would be Washington, DC. It's en route between New York and New Orleans, is an easy city for tourists to get around (good public transportation, well-located station, densely populated and good walking town). Of course, the big draw is the White House and other government buildings, but there's also a lively cultural scene, some great museums, theatres, live music etc. Other major cities that you're be passing through on this leg of the trip will be Philadelphia and Atlanta, but I haven't been to either, so will let others speak for them.
One more thing -- I do think that it's a shame your itinerary doesn't include any of the western trains. The scenery in the Eastern part of the US and the Midwest that you see from the trains are pretty, but not particularly different from what you see in the UK. The swamp/bayou areas around New Orleans are unique, but you don't get to see a whole lot of that from the train (you should, however, do a swamp tour from New Orleans). By contrast, the Western trains cross through the Rockies, the deserts, the high plains: terrain that feels completely different from you have in the UK. If you want to see what I mean, take a look at these pictures taken from two trains, the Lake Shore Limited from New York to Chicago, then the California Zephyr from Chicago to San Francisco.
http://www.seat61.co...rnia-zephyr.htm . It's a personal choice, but I enjoy the scenery of the western states much more. However, including the west coast would mean you'd have to look again at your whole itinerary. And, of course, the skylines of New York and Chicago are a spectacular sight in themselves.
