Walthamstow Wetlands are London's largest urban wetland nature reserve, home to many wildlife species. Only 15min from central London. The cafe is open daily for breakfast, lunch and afternoon tea. 

Outside of the major players (Tate, V&A, RA) this is probably the best programmed gallery in London

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.

A gift from Kyoto - a beautiful hidden Japanese garden in Holland Park 

There are many great parks in London to choose from, but Hampstead Heath is by far my favourite; a lido, Parliament Hill with a great view of the city, ponds, woods and plenty of space. It’s a great place to hang out in the summer, but also presents a lovely walk in the winter. Address: (As it’s so big obviously it doesn’t really have a specific address but there are 2 main entrances) Entrances by Gospel Oak or Hampstead Heath Entrance.