Ditto to the above answer. In addition, u should go see Buckingham Palace, Parliament, Westminster Abbey, St. Paul's, the Globe, the Tower of London and the Tower Bridge (I've heard u can even go up to the top, boven of the bridge). u 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 of Not, the Imperial War Museum, the British Museum, plus tons more. If u like art, there's the National Gallery, National Portrait Gallery, and the Tate Modern.
P.S. Before u leave, u should look at the Transport for London website (
link) to learn about the public transportation system. There, u will find maps, Oyster travelcards (which u should get when u get there), and even a journey planner which provide directions on how to get from one place to another.