Ooh, thanks for the tips!

You should see Trafalgar Square for sure, it's a beautiful open space and right in front of the (free!) National Portrait Gallery/National Gallery. In walking distance from there is Leicester Square, Covent Garden, and Piccadilly Circus. And I assume from your interests that you are a fellow geek, so Forbidden Planet (http://www.forbiddenplanet.com/WhereWeAre.html) is definitely worth checking out. Big Ben is also worth a visit, and Westminster Abbey is right next to it (admission to Abbey is 10 pounds, and I think it is closed Sundays for worship). And make sure to see the British Museum! Their exhibits are vast, and they have the Rosetta Stone.

Having some sort of street map helps a lot; London is a fantastic city to get around on foot in, and a map helps you get to where you want to go right away (the streets can be confusing the first few days). Even many native Londoners carry street atlases because there are so many random side streets!

Never a visit to London without the Forbidden Planet! *cough*