My favourite library when I was a student, I still love to wander and look up to its Renaissance sculptures. 

East london spot with a bit of everything, food during the day and cocktails, music and cinema during the night. Few nice places around like E5 bakery, Netil 360 rooftop, and Mare Street Market

Nice place for a cake and coffee.

Maybe an obvious choice, but the Barbican is always good. My favourite space in there is the curve gallery, last time I went was for Cory Arcangel's 'Beat the Champ'. I love the architecture, although not many people do. I think it was voted 'London's ugliest building' in 2003.

The best thing about any charity shop is that you never know what you are going to find. I have a well tested route around London that includes all of my favourite charity shops. This Oxfam has a great selection of books and often turns up some interesting clothes too.