Well, you have many choices, it all depends on what you're interested in!
How about these for starters?
Buckingham Palace - where the Queen of England lives.
Houses of Parliament - the 'mother' of parliaments where democracy rules!
London Eye - great wheel with capsule pods to give you breathtaking views of the city.
Tower Of London - a fantastic 10th century (?) castle/fortified building next to the River Thames. The Crown jewels are kept here.
Tower Bridge - gothic bridge spanning the river, spectacular architecture.
Madame Taussauds - wax models of celebrities and historical figures.
Tate Modern - all the latest cutting edge art in one great brick building.
Globe Theatre - replica of Shakespeare's theatre, a beautiful wooden building where plays are performed year round.
West End - theatre land - the world's greatest theatres and actors waiting for you!
PUBS - London has many historic pubs (see my hub!) superb venues for a drink and a chat.
Wembley - sports stadium, state of the art - pop groups play here too.
Stratford Olympic Park - east end of the city, great stadia and venues for all kinds of sport and entertainment.
That should be enough to get you going!