Dufftown is a burgh in Banffshire, Scotland, that, according to Hermione, is "not very far" from Hogwarts Castle. This burgh became notable for being one of the only places Sirius Black was ever sighted after his break-out from Azkaban. 
Sirius Black's sighting
Sirius Black was sighted in this burgh on 9 September of 1993, by a Muggle woman. She called the Crime Watchers Hotline, a special hotline to report sightings of Black. The Ministry of Magic was automatically alerted and Cornelius Fudge (then-Minister for Magic) dispatched hundreds of Witch Watcher Special Forces to the village, as well as hundreds of Dementors. This proved unsuccessful, as Black had already left when they got there. Furthermore, the population of Dufftown panicked when the Dementors arrived, so the Special Forces took more than four hours to calm everyone down.
- Harry Potter and the Prisoner of Azkaban (Mentioned as "Not too far from here")
- Harry Potter and the Prisoner of Azkaban (film) (Mentioned only)