The National Museum of Computing at Bletchley Park. Some of it's housed in the old huts used by the wartime code breakers, which is a bonus. They're in the process of improving the visitor experience, which makes sense. Nevertheless you should get there before they do because it's bound to be dumbed down eventually.
We went on an organised tour which meant we were conducted round by volunteer enthusiasts, many of whom I would guess are in their sixties. That means that when they started work - in one case as an actual rocket scientist - they were lucky to be issued with a calculator and have since seen at first hand the growth of an obscure branch of science into something without which we would have trouble getting through the day.
They lead you through rooms cluttered with improbably huge and clunky machines which would take days to perform a piece of long division we can now do on our phones. They have machines that take discs the size of Redwood trees and can only be turned on for five minutes a year for fear they drain the national grid. They have a card index system used by a chicken farmer in the early 50s that cost millions of pounds in today's money.
They explain it all with the ease of people who've spent some time under the bonnet of even the most improbable main frame. These blokes are as essential a part of the museum as the exhibits. In twenty years time their parts will be taken by actors. Get there before that happens.