The Almeida, in Islington, is a small theatre with big influence. It's an intimate place to discover groundbreaking theatre and get up close to some of Britain's leading actors. The cafe/bar across has a constantly-changing tasty menu, relaxed atmosphere and free wifi. Open all day and great place to spend time even if you're not going to catch a production.
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)
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.