Thanks for the advice. Hopefully I should get down to planning it in the summer and do it next year. Unfortunately it will have to be in the summer months, but I may be able to do it as late as September or October, so hopefully this may mean cheaper hotels and less tourists. Most of the trips on the east coast can be done in a day, with some in as little as 2-3 hours, which is good.
A vague route what I have in my mind is:
Boston
New York
Philadelphia
Baltimore
Washington
Pittsburgh (maybe)
Cleveland
Detroit (will have to take bus connection)
Chicago
Seattle (might break someone in between. Any idea what Minneapolis is like?)
San Fransisco
LA
Las Vegas (but not too sure, may miss this out)
Houston
New Orleans
Atlanta
and somewhere after that!
This is around 16 places, so that should be just about covered by 18 segments, but could but tickets to make up for any over-runs. Probably planning to spend 2-3 nights in some of the major places, with a day or two for others.
I'm not planning on upgrading for the sleeper compartment to keep costs down, and don't particularly like the idea of sharing with someone else. Long train journeys don't both me a bit, although the Chicago - Seattle one looks very long, so may break in the middle.
I have some money saved up from work, so was guessing at a rough estimate of around £3,500 including the ticket and flights. Does this sound reasonable? I haven't checked it all through yet but this sounds like a realistic figure.
Still, early stages yet, just playing around with ideas.