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.
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 :)
The Barbican has so much to offer! From beautiful architecture, to a conservatory, amazing art, films, music and performances. It is such an exciting and relaxing place to hang out. Even if you don't have a purpose for visiting the Barbican, it's good for just having a tea with a friend.
Paul Rothe n Son has been there 120 years, bang in the middle of town. Hard to find a proper old-school deli in central London nowadays, n none more proper than this place. Great jacket potatoes, soup, sandwiches. It looks the part too. And the service is always great. Try and avoid the lunch queue.