Some recommendations of things I enjoyed when I worked there a few years ago...
- Visit the British museum (it's huge), and the Imperial War Muesum (slightly less huge). Both shouldn't be missed.
- Have a pint in Leister Square or anywhere, and enjoy the pub food.
- Take in a show?
- Very Greenwich Observatory to step across Earth's dividing line.
- HMS Belfast
- Tower of London (a bit pricey for what you see though)
- Watch tourists get crapped on by pigeons in Trafalger Square
- Buckingham Palace (the outside is a bit dull though)
- 10 Downing Street (can't get too close though)
- Horse Guards at Whitehall
Things to skip:
- The wax museum
- The London Dungeon