Where is "Macbeth's" castle located?

Inverness Castle sits on a cliff overlooking the River Ness in Inverness, Scotland. The red sandstone structure, displaying an early castellated style, is the work of a few 19th-century architects. William Burn (1789-1870) designed the Sheriff Court, Joseph Mitchell (1803-1883) the bastioned enclosing walls, and Thomas Brown II (1806-1872) the District Court, originally built as a prison. It is built on the site of an 11th-century defensive structure. Until March 30, 2020, it housed Inverness Sheriff Court: this has now been moved to the Inverness Justice Center.

In Shakespeare's Macbeth Inverness Castle is the site of Macbeth's murder of King Duncan, allowing Macbeth to usurp the crown. It is also where Macbeth's descent into madness plays out, with many key scenes happening within the confines of the castle. Much about the actual history of these individuals is different from how Shakespeare's drama plays out, for example, Duncan was murdered at a much younger age than Shakespeare portrays, but the characters and locations can still be fixed, to some extent, geographically and historically.