The above are good suggestions, don't miss the Natural History Museum if you're in the area.
For interesting trinkets and shopping head to one of the markets. I would recommend going to Borough Market near London bridge (Sat only) and then hopping on the train to Greenwich which is well worth a visit. They have a market Sat and Sun (take the mainline train from platform 1 or 5 at London Bridge).
Alternatively you can walk along the South Bank from London Bridge and take in the Oxo tower, Tate Modern and have a nice lunch at Gabriel's Wharf, or outside the National Theatre before jumping on the tube at Waterloo. (There's a huge book market under Waterloo Bridge (mostly crap, but you never know what you'll find)
DO NOT go to Oxford St., Bond St, Knightsbridge, King's Rd., Leicester Square and consider skipping Covent Garden too. If you're on this site, they will probably be your idea of hell. That's if the whole of central London isn't already.