Science Museum is one of my favourite places in London. They have a wicked aircraft section with all sorts of planes and bits and pieces. Besides the aircraft the rest of the museum is very modern and very enjoyable. Best bit is it's free (though I'd leave a couple of quid donation if you were as impressed). I pop in there every time around that area of London. Also it's literally right next door to the
Natural History Museum as well (both opposite Imperial College, which I suppose makes it roughly the Kensington area).
From both these you are just a short walk north to Hyde Park if you want to go some greenery. And if you are into art kind of stuff it's not too far from the
Victoria & Albert museum, perhaps not my favourite place but I know people that enjoy it there.
I know it may sound boring suggesting two museums, but I think they are well worth an afternoon or morning of your time as both National History and Science Museum are free and next door to each other. And Science Museum rocks
