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)
I've had a love affair with the BT Tower for some time now. Unfortunately entrance to the public was shut in 1980, but earlier this year I was invited up to the top, where the revolving restaurant once stood. The views were absolutely breath taking.