As a general principle, castles tend to be on hilltops, where they can best defend against hostile attacks, and Edinburgh Castle is no exception. Along with the defensive advantage (besieged 23 times, captured only three), comes an impressive set of views.
The parkland below, Princes Street Gardens, was a large artificial lake that helped defend the Castle until the middle of the 18th century, when it was drained as part of building the New Town, which lies just behind it.
These are a few images, mostly of Edinburgh’s New Town, from various parts of the Castle. Had I thought about this in advance, I might have climbed other parts of the Castle for views of the Old Town as well. Behind the buildings of the New Town the vista stretches to Leith and the city’s port on the Firth of Forth. 
Looking down into the gardens, the main rail station Waverley, is part of the view; the rail line runs through the bottom of Princes Street Gardens. Waverley is said to be the only rail station in the world named for a novel, this one by Sir Walter Scott whose monument is nearby. Princes Street, along the gardens, is constantly full of buses and trams.
These two views, taken through former gun ports, are of the newer portions of the Old Town.
Edinburgh is such a lovely city. Thank you for the great photos!