What are you into?
Go to the theatre I suggest to see a show.
I would definitely plan for a day outside of London and maybe head down to Cornwall or somewhere and spend a day or book a B&B and spend a night. It's beautiful down there and if its warm go to the beach in Cornwall as they are beautiful!
Greenwich Park/Hyde Park
Brick Lane or Camden
Westfields Stratford for some shopping if its cold out or Oxford Street if its okay
Check out the museums and galleries if your into that
Go on an open top bus tour and learn some history
London Dungeons or London Bridge Experience
The Jack the Ripper Tour
Thames Boat Toar
Your spoilt for choice in London and I can't name or think of so many things that are possible to do!!
Check out http://www.timeout.com/london/
gives you a great selection of any events or any must sees in London.