The fun bits of London are mostly all within 5-10 minute walking distances of each other, and the London Tube (underground) transit system is great (when not on strike..).

So.. you can stay almost anywhere and be happy.

I have stayed in London twice, both times just a 30-second walk from Trafalgar Square in the heart of London. The hotel was *cheap* by London standards, yet clean and modern enough to please.

The place was the "CITADINES TRAFALGAR SQUARE", which you ought to be able to find online. Rates were US$120/night when I stayed there, which is exceptionally cheap!

Cheers