Mine would be the Oxford University Museum of Natural History, the Natural History Museum in London and the Imperial War Museum.
The first two are pretty similar in theme, but I prefer the Oxford NHM over the London NHM because it is considerably calmer, and with more interesting specimens (especially dinosaur skeletons!
). The London NHM is bigger and has a lot more, yet it is busier, and I once went there to see the new dinosaur exhibition, but there was a two-hour queue
leading into there! Heck, that was a nightmare (worth it, though).
The IWM has lots of interesting exhibits, my faves being the Holocaust exhibition (it teaches you about the Holocaust in vivid
detail) and the two live exhibits on the Trenches of WWI and the London Blitz of WWII (you enter them and get a realistic sense of what it was like in these environments!
Coming at a close fourth is the British Museum. I would also include the Anne Frank House in Amsterdam, the Museum National d'Histoire Naturelle in Paris and the American Natural History Museums, once I have visited them.