Spacious bar and dining place with a scandinavian feeling to it. Different independent shops like record shops, flowers, etc inside the place. Pizza is good!
I can't pass without dropping in, Orcs Nest is a small independent boardgame, D&D etc store that's been around forever(1987)... and has the best logo. Good selection of games for younger kids too.
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.