Aside from the excellent cultural facility's the Barbican Centre has to offer, ranging from theatre, art, music and dance. The space outside the Centre holds personal value in its ability to evoke nostalgia of the Emerald City, in the slightly disturbing film 'Return to Oz'. I enjoy residing by the fountains, where I draw, read books and feed ducks.
If you want a peaceful day out of the busy city, Highgate doesn't really feel like London. The cemetery is interesting and peaceful, there's a tour of the old half which is definitely worth the money. Karl Marx, among others are buried there.
SOAS university has a small gallery space dedicated to exhibitions about Asia, Africa and the Middle East. There's a small but beautiful Japanese zen garden on the rooftop (currently closed for refurbishment)