I love the George and Dragon Public House. Cluttered deco of silly artifacts and memorabilia and slightly scuzzy around the edges. Great drinking characters, DJs and The White Cubicle gallery in the ladies toilets is difficult to beat.
London has plenty of beautiful cemeteries. Brompton is one of the ‘Magnificent Seven’ and has many interesting tombs. It was also an inspiration of names for Beatrix Potter and the resting place of Emmeline Pankhurst.
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 Hayward Gallery in Southbank center has held my favourite exhibitions in London and each time they are extremely well curated. Definitely a place to visit !