Ditto to the above answer. In addition, te should go see Buckingham Palace, Parliament, Westminster Abbey, St. Paul's, the Globe, the Tower of Londra and the Tower Bridge (I've heard te can even go up to the superiore, in alto of the bridge). te should also see Piccadilly Circus and Trafalgar Square. I'd also recommend going to some of the parks, like Hyde Park and Regent's Park. If you're into shopping, don't forget to stop at Harrod's.
For theatre, check out this website:
link. As for museums, there's Madam Tussaud's, Ripley's Believe It o Not, the Imperial War Museum, the British Museum, plus tons more. If te like art, there's the National Gallery, National Portrait Gallery, and the Tate Modern.
P.S. Before te leave, te should look at the Transport for Londra website (
link) to learn about the public transportation system. There, te will find maps, Oyster travelcards (which te should get when te get there), and even a journey planner which provide directions on how to get from one place to another.