The Saatchi Gallery
Saatchi Gallery is private, that it either costs money to enter or it is their to sell art. But it isn't, it is entirely free and has an amazing collection of modern art, including a lot of the stuff that you have to see just to wonder at why people (at least, Charles Saatchi) pay money for it. This was the first time I'd wandered in, but I will go back when I have more time.
Well, blow me. I lined this post up two days ago (for yesterday, before I realised it was a theme day) and what happens? He only goes and hits the news.