A cool Geeky place to go is the Science Museum
http://www.sciencemuseum.org.uk/ in Kensington which is one of the best in the world. With the National History museum http://www.nhm.ac.uk/ next door you'll easily have a good time and no doubt learn a few things ...
and it's all free!
Also what i suggested.
It was the best i saw in london, when i was there!