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 Royal Park offers great views of London and the city; As well as housing the Royal Observatory which includes a museum of astronomical and navigational tools, part of the National Maritime Museum.