There is no need to go far from the centre of Edinburgh to get panoramic views of the city and beyond as just a very short walk from the main bus and railway stations and shopping area is Calton Hill which became one of Britain’s first public parks in 1724. It is a place of several monuments and from there that the iconic view is often used in news reports of Edinburgh and the castle.  At a time when the Old Town of Edinburgh was very crowded and the New Town was being built the philosopher, David Hume in 1775 petitioned for  A circulatory foot road which would present strangers with the most advantageous views of the city  ….  and contribute not only to the pleasure and amusement, but also to the health of the inhabitants of this crowded city. 
 The shortest walk is up steps from Regent Road to the top although my favourite one is from the entrance near the Old Royal High School and along Regent Walk below the Nelson Monument and full of colourful flowers in May. Here is the view from there looking south over the roof of the old R H S towards Holyrood Park, Salisbury Crags and Arthur’s Seat.