Spent a semester in London, and there's definitely no shortage of things to do. If you like American-style clubs and are there over a weekend, Rouge (West End on Charing Cross Road) and Purple (underneath Stamford Bridge at the border of Chelsea and Fulham) aren't bad. If you like trance and underground, DEFEINTELY check out Turnmills and Fabric, both of which are in the East End.
There are also walking tours of different sections of London, which white alluded to. The most popular of those are the Jack the Ripper walk and the Beatles walk.