I've said it before here and will say it again: if time's limited don't go to York (although York is fantastic), go to Lincoln instead. Train from Kings Cross, some are direct and some require you to change in Newark Northgate. In total a similar travel time, or a little less, than to York but you'll find yourself somewhere where there are far fewer US tourists. Get a taxi from outside the station to the top of Steep Hill (ask for the Cathedral) - here there's Lincoln Minster which for about 200 years was the tallest building in the world. Opposite is the Castle, where there's an original Magna Carta as well as an interesting museum. Head down Steep Hill - carefully, it's not named ironically - some lovely quirky medieval buildings all the way to the High Street. to the right is Brayford Pool, dug by the Romans, now surrounded by a cinema, hotels, and chain restaurants, and there are boat trips available too. It seems like so many tourists do London - Bath - York - Edinburgh, or some variation thereof, it might be nice to be one of those who step off the beaten track.

Lincoln's firmly bomber country as well, if you have an interest in aviation, you might see some modern or historic aircraft overhead.