Beautiful, striking countryside surrounds Edinburgh in every direction. The Pentland Hills to the south of the city are a decent hike and provide magnificent views back over the city and Firth of Forth. Also, some way south of the city, at Roslin (about eight miles: take the southbound Lothian bus No.36 from North Bridge), there’s a fantastic 15th-century chapel founded by a Prince of Orkney; the amble all the way down Roslin Glen from there is quite breathtaking.
Depending on the weather, a refreshing walk along the barren East Lothian beaches between Aberlady and North Berwick will either blow the cobwebs away and leave you with a rosy, healthy glow, or give your face a thorough sandblasting.