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.
You would have seen the Brutalist towers and curves from afar. Upon entering the estate where the cultural centre is, you quickly realise the scale, the beauty and charm of this labyrinthine project. Barbican Centre's programming is top of the league across art, theatre, dance and music, both contemporary and classical, art forms. This place is an architectural and cultural institution boldly redefining the UK's cultural landscape.
Key community arts centre, near to Shoreditch High St station. The cinema is handy and the music programming is solid, but they also host a variety of other interesting nights, most notably Jawdance, London’s (arguably) best spoken word night
Half a mile from Markfield Park down the River Lee is Springfield Park. The park rises steeply up from the river and has an amazing array of tree species making it beautiful in all seasons. At the brim of the hill there is a line of park benches each one surrounded by box hedge offering a private view across the Lee Valley, Walthamstow and beyond. The park warden was nice enough to give me a chestnut log a couple of years ago from which I carved a bench and two stools.
This vegetarian south Indian is a bit of a hidden gem, good curry friendly staff very reasonable with bring your own booze doesn’t get much better than that.