The AA is Britain's oldest school of architecture, but anyone can take advangte of the great work going on there. You can catch really interesting public lectures and free exhibitions throughout the year. There are also occasional installations and event launches, a bijoux cafe and brilliant bookshop. A great place to hang out with the builders of the future.
The Barbican has so much to offer! From beautiful architecture, to a conservatory, amazing art, films, music and performances. It is such an exciting and relaxing place to hang out. Even if you don't have a purpose for visiting the Barbican, it's good for just having a tea with a friend.
The Almeida, in Islington, is a small theatre with big influence. It's an intimate place to discover groundbreaking theatre and get up close to some of Britain's leading actors. The cafe/bar across has a constantly-changing tasty menu, relaxed atmosphere and free wifi. Open all day and great place to spend time even if you're not going to catch a production.
A brilliant little hidden gem of a place to relax and look at some interesting rare / Out of print books and Magazine. Their evening art events are also very special. Great atmosphere and great people.