I'm not from London and only have limited experience of it myself but I would definately say if you have the time go to see a show in the West End (UK equivalent to Broadway), Oxford St is supposed to be the place for shopping. The Millenium wheel is a must as a trip down the River Thames providing it is not too bad weather. I haven't been myself but the Tower of London is supposed to be very good. There are numerous museums that are free to enter (e.g natural history museum, Imperial War Museum). Nelson's column is quite spectacular. At certain times of the year you can go into Buckingham palace and the Houses of Parliament but I don't think they are open to the public now but it would be worth checking as both are extremely good tours.
Hope this helps.
Me 43 XH 45 M 2.7.88 Divorce 7.10.09 Kids D20,S17 & D15