The walk along the South Bank from Westminster to Tower Bridge will take you past a plethora or interesting sights and cultural hotspots. There's always something interesting going on too.
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.
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...
One of the main sources of inspiration for my work are unusual objects, vintage toys and tools. A great place to find them is this genuine car boot sale, which is clear of 'bargain' toilet paper and questionable cosmetics. Another plus are the comparatively sociable opening hours. (it starts at noon… )