My order of preference:
Must see inside of Westminster Abbey. It is amazing. I can't believe that they let people in there.
British Museum. Want to see the Rosetta Stone, the outside of the Parthenon, guardian statues from city walls in ancient Assyria, items that are 1000's of years old, and a million other jaw-dropping pieces of history?
The Tower of London. William the Conqueror's castle beachhead.
The RAF Museum London (Hendon). Has the world's last remaining Typhoon plus lots of other nifty WWII aircraft.
The Churchill War Rooms. Where Churchill and the senior staff administered WWII, and where Churchill lived.
Also, in London, get fish and chips, an English breakfast, and a good curry.
London is awesome.