Hmm...look Posie up?
Seriously, London is one of those cities you could spend a week in and still have things left over. I have been there 3 or 4 times and have yet to see the British Museum, believe it or not, from Mr. History Buff.
Westminster Abbey is likely #1, the Tower is cool, Buckingham Palace, you know, the usual touristy stuff. They also have lots of pub walks, Jack the Ripper walks -- local lore kind of things, going on at night. Once again, touristy, but entertaining.
The tube is great for getting around, but for short distances, you might enjoy it more to be on the streets walking around. See more stuff, plus those little vignettes of British civility and tradition in people's daily interactions...
worldwidemike, himself a tradition in civility