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).
There are not many places in London like it. On a Saturday during market hours it heaves with stalls and visitors for a good mile or two. Great place to pick up some bric-a-brac, genuine oddities and a great bite to eat, or just enjoy the hustle and bustle vibe of the place.
It is a music store in Brick Lane. You can spend there the perfect Sunday afternoon, listening to lot of new good music, thumbing through cool books while relaxing in their café. Oh, and the Rough trade photo-booth is a must if you go there!