I lived in London from this past september to january, and it blew my mind. There was something to do every single night, if I only had money for it. There was at least 1 if not 3 or 4 concerts a week that I was interested in, and about 10 indie-rock nights of the type like Liberation Dance Party, or Mousetrap to choose from. Any day of the week too. I quite liked Panic! At the Roxy just off Oxford Street. They made the best Long Island Ice tea for cheap (7 quid for a pitcher). The museums are amazing, tate britain, british museum, and the national gallery being my top picks. Parks are great, I frequented Primrose hill and Hampstead Heath mostly as I lived in Camden Town. Which is amazing for the markets and cheap good food. Def go to any football match, it's the basic British experience. Pubbing is a must, for trying all the different real ales can be extremely rewarding. Plus, from London you can catch a coach for extremely cheap to many areas quite far from the big smoke itself, Oxford is a fiver away.