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.
The Wellcome Collection is a free museum and library, mostly dealing with medecine and social history. The exhibitions are unusual and engaging, and the permanent collection includes bizarre items such as medieval masks and human remains.
An unassuming glass door on an otherwise plain facade hides a cavernous space, with high ceilings and huge sliding partitioned walls producing excellent exhibitions in a space you'll want to go back to.