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