I go to the Heath every weekend (often via the wonderful Waterlow Park which skirts Highgate Cemetery) and during the week too if I’m working from home; it helps to put things in perspective when I’m thinking about my work. It’s great in the summer for obvious reasons but I love it the most in autumn and on those rare days it snows so much London grinds to a halt (which doesn’t take much). Everyone heads up there to make giant snowballs/cats/creatures and surf down Parliament Hill on anything they can get their hands on. Grown ups turn into kids for the day. My husband and I made this snow yeti last year, it was sad to leave him behind but he soon made friends and even made it into the Camden New Journal.
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.