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.
There's something so quintessentially London about this hill. The network of paths and lines of lampposts leading you up to a view of the city that's at your fingertips.
The Bun House is one of my favourite places in Peckham. It’s a local pub and art project space. The sense of community and the warm heartedness of everyone, especially Mick (the owner!) are truly genuine. Various events, performances and exhibitions populate the project room, the pub’s drinking zone and the outdoor rooftop terrace at the back.
Leila McAlister's grocery shop and café off Arnold Circus, Shoreditch. You can find the best of everything, from jars of horseradish to eggs and croissants.