Not the most exciting place inside, but a lovely rooftop area which not all that many people seem to know about, 2 mins walk from Old St station. If it’s packed then The Red Lion is just up the road.
Slightly biased as this is where I live, but Stoke Newington is great place to spend lazy saturday / sunday afternoons getting sloshed with friends. There are 10 + pubs within walking distance who all are great places for one reason or another. I'll pick out the White Hart for its huge beer garden...
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.
Aside from the excellent cultural facility's the Barbican Centre has to offer, ranging from theatre, art, music and dance. The space outside the Centre holds personal value in its ability to evoke nostalgia of the Emerald City, in the slightly disturbing film 'Return to Oz'. I enjoy residing by the fountains, where I draw, read books and feed ducks.