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.
This independent cinema near Angel in North London is over 100 years old and has had several lives including hosting early Sex Pistol gigs. It now serves as my favourite place to watch films (along with the Rio in Dalson).
Frank's bar opens on the roof of a multi-storey carpark in Peckham every summer. It's great to go for a drink and get this phenomenal view of London. I love the design of the bar, which is different each year, and the exhibitions are always interesting.
Slightly biased as this is where I live, but Stoke Newington is great place to spend lazy saturday / sunday afternoons getting sloshed with friends. There are 10 + pubs within walking distance who all are great places for one reason or another. I'll pick out the White Hart for its huge beer garden...