I would download several self-guided walking tours from iTunes and spend several hours just walking, looking, observing...and popping into some pubs. I'd certainly take in some of the sites that ajax mentioned as well but having seen them all at least once, I really enjoy just walking around and seeing lesser known sites and picking up a bit of the back story as well. London is dreadfully expensive, but almost all of the sites ajax lists are free so that makes it easy to pop in to them and spend 30 minutes before moving on. I tend to pop in to the British Museum to see the Rosetta Stone and the mummies each time I go as well as spend some time in the National Gallery.