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.
My all-time favourite place. Whitewashed ex-smokehouse where Fergus Henderson pioneered the resurgent interest in offal dishes. The restaurant is brilliantly unfussy, retaining lots of the smokehouse’s original features, and the food very British, making St. JOHN something of a London institution. The restaurant has a winery and bakery.
Nice old trees, lots of space, good for walking, running, hanging out with your kids and most of all, the perfect place to lie in the grass and chill out.
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).