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)
The AA is Britain's oldest school of architecture, but anyone can take advangte of the great work going on there. You can catch really interesting public lectures and free exhibitions throughout the year. There are also occasional installations and event launches, a bijoux cafe and brilliant bookshop. A great place to hang out with the builders of the future.
Beautiful museum with permanent collections on anthropology, natural history and musical instruments. Surrounded by a park with farm animals and beautiful views of London skyline.