My favourite restaurant as the moment which was a former boxing hall. You sit on the old spectating seats and get served butter chicken on pine cones which infuse their flavour into the food. A really different experience.
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.
If you like some nice cool beer, portuguese sweets (the once with yellow custard inside) tasty and affordable sandwiches, good strong coffee and football, at all hours. Max Snack Bar is worth checking out.
London has great green spaces. There are large royal parks and small public gardens, hidden allotments and roof terraces. Each one has its own identity and characteristics and everyone has their favourite. In summer they become extensions of people homes, you see girls sunbathing from 9 am and the endless picnics mean you can eat 3 meals a day in the park. My favourites - St James Piccadilly Gardens, Hyde Park, Barbican Conservatory.