The second coffee shop has to be Kaffeine. Having only recently come across this one, I was certainly impressed and they may even have the best coffee I've had, since a short stay in Portland, Oregon.

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.

Eccentric and surprising house and museum of architect Sir John Soane. Mostly unchanged since his death over 180 years ago, it is full of atmosphere. Also have spotlit, late night openings.  

Key community arts centre, near to Shoreditch High St station. The cinema is handy and the music programming is solid, but they also host a variety of other interesting nights, most notably Jawdance, London’s (arguably) best spoken word night

A special place, a shop which is like a museum, worth popping in to feel the humanness and heritage of London. And if you are looking for rope, compass or any sailing supplies, this is the place. There is no shop like it.