Just above the Dorfman Theatre lobby at the National Theatre, is the entrance to the high-level walkway, a public walkway that overlooks the National Theatre props and scenic workshop.
It's free and is a unique chance to get a glimpse of what happens backstage. I love popping in when I'm on the south bank, as you get a completely different sight each time, depending on which production the workshops are working on at the time.
There are many quirky book stores in London, but I really love the selection that Daunt Books have, they often have bespoke editions which you won't find in other book stores. Also, the people that work there are so helpful and knowledgable. I can never stop myself from walking in!
Tate Modern can always be relied on for offering up interesting, challenging exhibits, housed in great architecture and with one of Londons best cultural bookstores. An ever reliable weekend hangout.
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)