I can definitely recommend a stroll in the Grassmarket, at any time. Unless you live in the old town, getting there on foot can feel like an expedition due to its steep approaches. The Mound, Candlemaker Row and Victoria Street are all moderate inclines, but the last two are also very charming.
Where is the Grassmarket? Well, if you lost your footing from the imposing Edinburgh Castle which overlooks the whole city some 300ft above street level, and tumbled down its southern rock face, you would come to rest in the Grassmarket area. A little bit shaken but hopefully still alive. Historically this area was a cattle market and a place for public executions, whereas today it’s an escape from the rigour of city-life, and a place to relax.
On a Saturday, stroll around the sprawling stalls of the farmers/craft market. Sit in a shady spot under a tree and watch the world passing-by (great for people-watching), or sit in the sunshine outside the many bars and restaurants. There’s often music playing from street performers, enhancing your experience.