I'm going there in less than two weeks. We planned to see the Kandinsky exhibit. (He's a great abstract painter). And to visit the theatre. And you could go on one of the bustours, it may sound cheesy, but it shows you everything eventually. ^^
I've heard the changing of the guards is really boring though. Don't go! And of course you could go shopping. :P
edit: I don't live in London, I'm just a tourist-to-be.
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I rocked my shoelaces untied
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