We had both already been to London, so we decided to only spend a day there, then goto other places that at least one of us had not been. This meant that we made the mistake of trying to rush around London, getting in a few sites in a single day. I do not recommend watching a play at the Globe -- standing room only -- after spending all night on a plane and all day walking around the Tower of London. By the time the play is over, you will be ready to fall over from exaustion. At least they give you a break at the end of every act instead of just one intermission.
Our particular crazy attempt to pack everything in aside, I highly reccomend the Globe, and the Tower. We also saw the changing of the guard at Buckingham palace, but be sure to get there a bit early so you can see. From previous trips, the British museum and Westminster Abbey are both must-sees, and a trip to Camden Town or Portabello Row is fun. Instead of Lunch one day, go to Herod's for high tea. You will stuff yourself enough that you won't need to have eaten before-hand. Also, London is a great place to see plays, so indulge your tendance for the theatrical.