What should I know about visiting London, and what should I do there?

I’m going to be in London for four months on a study abroad program (from the USA). What should I know about the city, and what should I make sure I do while I’m there?

Your answer might be “get a discount rail pass; you will save lots of money travelling to certain destinations,” or “take a walk in Regent’s Park on Sunday night; the atmosphere is beautiful.”

Your answers should not be limited to things about London: convince me to visit Wales, or something!