The Wellcome Collection is a free museum and library, mostly dealing with medecine and social history. The exhibitions are unusual and engaging, and the permanent collection includes bizarre items such as medieval masks and human remains.
The Premises is cozy café attached to a recording studio in Hackney (frequented by Nina Simone, Al Green and Jarvis Cocker over the years.) Lovely people serve up tasty breakfasts and Turkish food in the evening.
One of my favourite things about London is the underground transport system itself. I love the design of the information systems and the stations have so much history — some of them dating right back to the 1800s.
A great walk down an old abandoned rail way from Finsbury Park to Highgate. Most of the original platforms are sill remaining so its an interesting place to explore...