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.
I love the architecture of the Barbican - it is so important to its historical context, at a time when London was being shaped for modernity after the war - they also aspired to make it a bold art centre. We need bold, always.
It's a members-only library but you might be granted access with a research request. The writer's room is great but there's a few special, hidden corners among the bookshelves to tuck yourself away in.