Maybe an obvious choice, but the Barbican is always good. My favourite space in there is the curve gallery, last time I went was for Cory Arcangel's 'Beat the Champ'. I love the architecture, although not many people do. I think it was voted 'London's ugliest building' in 2003.

I’ve always been very fond of the ICA and its maverick spirit, less so in the latter part of this decade. These days the place is magnetic. To feel this incredible and unique place for arts and expression, breathing, breathing invigoratively, is rewarding to a London dweller or/and visitor. Its incredible transformation, revived from near death by Stefan Kalmár, is felt as soon as you enter the space, it feels open and alive, with vibrant and human energy in staff and visitors; risky, independent, engaging, resounding, and topical to our times programming, which is focused on breaking barriers in imagination an intellect rather than visitor record numbers. It is a breath of fresh air and an example what London art institutions are capable of if they open themselves to welcoming in an outsider and their passionate vision. And they have the best membership in town!   

It has such a special vibe, it is very near Columbia Road and Broadway Market It is surprising to find a farm in the middle of the city! Very recommended having English Breakfast there :)

Inspired by Dave Eggers’ projects in the USA such as the Pirate Store in San Francisco and Superhero store in Brooklyn, The Monster Supplies Store in Hoxton is home to the Ministry of Stories: A volunteer run organization, founded by Nick Hornby, to help young people with creative writing of all kinds through workshops and free mentoring sessions. The store is the “Purveyor of quality goods for monsters of every kind” with fascinating bottles and tins containing everything from eyeballs to Zadie Smith’s short story Mortal Terror.

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.