When I was in London a few months ago I took a day to go out to Bletchley Park. It's about a 45 Minute train ride from London Euston. It the place where Alan Turing and the code breaking team broke the German Naval Enigma Code.
Some of the buildings are rebuilt, but the mansion still stands and you can go inside, it's not a bad place to be.
If you're into Formula 1, Red Bull Racing is located in Milton Keynes, decently close to Bletchley. I know they used to do tours of some of the facility but unsure as to whether they do now.
My nerdiness also took me to the London Transport Museum Depot (not the actual museum at Covent Garden), which only opens intermittently and tickets have to be booked in advance.
If you're into aviation, there is also the RAF museum, which I thought was quite impressive when I went more than a decade ago.
You can be a real tourist and go to Greenwich, straddle the prime meridian so you're in both the western and eastern hemispheres at the same time.
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