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.
Though the city is amazing with a lot to offer, of course it’s great to have your own hideaway. My room is essentially my studio/desk space too and the hub of my creative activities.
This is the place where ghost pirates roam in times forgotten. Where great poems were once written. Everything has happened here. A few abandoned boats and much stillness. And an island in the middle. Most curious. Not much choice but to explore as far as your nerves will take you. Watch out for Zorro the dog.
The V and A houses a public collection of prints and drawings of every kind imagineable from old master drawings to photographs, playing cards, fashion plates and wallpapers. You have to select what you want to see from the collection http://collections.vam.ac.uk/and book in advance. The behind-the-scenes route up to the study room of v and a is a treat alone (pictured)
Not the most exciting place inside, but a lovely rooftop area which not all that many people seem to know about, 2 mins walk from Old St station. If it's packed then The Red Lion is just up the road.