York
There are very regular fast trains to York from King’s Cross station. Journey time is around two hours. Prices can be high as it is a popular route, continuing on to Newcastle and Edinburgh, so you are advised to book as early as you can, get a reservation and a good rate.
York is famous for its old and wobbly streets, the ruins and museums, the river and the minster (cathedral). Also for its rip-off tourist shops and so-so tea rooms.
In 1984, the Jorvik Centre opened. If you don’t mind the silly mannequins, it is a very interesting place, but book in advance.
If none of this appeals, there’s the free National Railway Museum, just by the station.