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