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 Hayward Gallery in Southbank center has held my favourite exhibitions in London and each time they are extremely well curated. Definitely a place to visit !
If they only could mend me like they mend my shoes. A three generation family business with its origin on Cyprus via Fifth Avenue, New York. They can do magic. I have been going there since I moved to London 12 years ago. One day soon I am going to have them make me a brand new pair of brogues. I will design the holes.
I spent a lot of time in the British Museum whilst studying for my Degree. My work has changed considerably since then but it is still a place I return to again and again. Inspiration doesn't always come from objects in the collection but also from the space and its visitors.