If you want a peaceful day out of the busy city, Highgate doesn't really feel like London. The cemetery is interesting and peaceful, there's a tour of the old half which is definitely worth the money. Karl Marx, among others are buried there.
Travelling on these uncrowded river buses is such a relaxing way to see the city's landmarks from the Thames. A really quick and lesser-known way to travel from central London to Greenwich, especially on a sunny weekend.
SOAS university has a small gallery space dedicated to exhibitions about Asia, Africa and the Middle East. There's a small but beautiful Japanese zen garden on the rooftop (currently closed for refurbishment)
Bulk Market is a zero-waste shop in the arches next to Hackney Central station. The shop offers a range of products such as fruits, vegetables, nuts and grains all free from any packages. Bring your own empty jars and reusable boxes.
A walled secret garden, the Physic Garden is like a time capsule, founded in 1673 to allow apprentices of the Worshipful Society of Apothecaries of London to study the healing properties of plants, it is now a living museum. Tours are offered by volunteers with immense knowledge of botany and the cultural history of the garden or visitors can wander the grounds alone and spot odd and fascinating plants such as the mystical Mandrake.