That's rather like asking what to do in NYC; personally, I say just grab an underground map and start going places. See Trafalgar Square, Piccadilly, etc. This is what I'd do, if you have time:
- See the changing of the guards.
Here you go. It's a tourist trap obviously, but it's fun to see.
- Madame Tussads. A lot of people seem really fascinated by it. It doesn't interest me much.
- Walk around the Thames, see Big Ben, Parliament, Tower of London, Tower Bridge (not London Bridge), etc. You could perhaps ride the London Eye. Again, a tourist trap, but fun enough and the view is great.
- Eat. Plenty of restaurants around. I'd hit some of the great Indian restaurants and some of your more ethnic places. I had great food while in London, everything from Egyptian to Ethiopian.
- See Westminster Abby. Darwin is there, Newton, etc.
That pretty much covers the touristy attractions. I'd mostly suggest just walking around and having a good time; of course, that depends on where you are, but that's where the Underground map comes in.
In summary: Go explore.