A great place to start the day if you are in South London is Federation Coffee in Brixton Village. The food is great and so is the coffee. This is a very chilled place where you can get both and indoor and outdoor experience (even though the whole place is under the Village roof).

Home to hundreds of stray cats and dogs. 

A lovely healthy cafe in portobello!

Some places are better to be left a secret. This one e.g.

The Design Museum is a museum in Kensington, next to Holland Park, which covers product, industrial, graphic, fashion and architectural design. There is also a nice cafe on the 1st floor with beautiful views of the park.