here's what I would do if I had british money:
drive around florida for a little. go to miami if you like to go out at night.
fly north to D.C. (it's super cheap) go to the museums. you could spend a day you could spend a week.
rent a car drive to baltimore (it's real close to D.C.) see the inner harbor and the aquarium. (that aquarium is top notch.)
drive 2 hours up to my home town Philadelphia for a day, then eat like a pig. get a cheese steak, some soft pretzels and water ice then...
take a hour and a half drive to new york city in the afternoon. stay for a few days.
drive up to the new England area a few more hours. ditch the car.
I'd say you could probably do the north east coast and see a lot in a week and a half. do all your driving at night the scenery is nothing to gaze upon. get a car with good gas mileage and it'll be pretty cheap.
fly to chicago or
fly to New orleans. see that area for a bit.
maybe fly up and see yellowstone
maybe fly to denver, rent a car and make your way around the south west
Some people might skip the northeast because they are starting in orlando, but c'mon pounds are pretty much double the dollar at the moment. take advantage of that.
but yeah I echo the other post as far as trains in america...way too much money. book greyhound buses in advance and you get them cheap. flights as well, but keep in mind the shuttle fees to get to and fro the airport. most buses stop in the middle of town.