The last time I was there, there was an HMS ship docked between the London Bridge and the Tower Bridge, which you could tour. Was cool.
Notting Hill is kind of cool -- neat parks you can explore, and some good British pubs
Tower of London -- you can see all the instruments of torture and meet some really *cool* ravens.
Visit a few pubs -- eat some spotted dick or fish and chips and drink a few beers. Good stuff.
But if the British ladies attack you, don't believe it when they try and convince you that snogging is a British tradition.
See the Changing of the Guard at the Palace. Try to kiss one of the guards and see if he moves (mine did. he smiled)
Churchill's War Room -- a coupl eof blocks from the Palace -- had a lot of WWII related memorabilia (a fave of Mr Osuche)
The big park near the Palace has some really pretty lakes, and features a pair of black swans (or at least it did when I was last there)