There are many quirky book stores in London, but I really love the selection that Daunt Books have, they often have bespoke editions which you won't find in other book stores. Also, the people that work there are so helpful and knowledgable. I can never stop myself from walking in!
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.