Glamis Castle in Angus, the childhood home of the late Queen Mother, is said to be one of the most haunted castles in Scotland. There the family chapel is haunted by a Grey Lady, who is said to be the spirit of Lady Janet Douglas, burned at the stake as a witch and also a young black boy who was badly treated haunts the door to the Queen's bedroom.
The ghost of Castle Fraser. located in Aberdeenshire, is reportedly a murdered princess whose body was dragged down a stone staircase leaving a bloody trail behind.
Of course, Edinburgh is positively bursting with ghosts and apparitions, and the Castle on the hill is not exempt from a haunting or two. The graveyard at GreyFriars is said to be haunted by the evil "Bluidy" Mackenzie who pursued Convenanters and tortured them. Then there's the Edinburgh Vaults, Mary King's close, Charlotte Square, Festival Theatre, the Radisson Blu Hotel, and so on and on. There are tours you can take to visit some of these locations but it's really fun and spooky to try it on your own. And no, I haven't yet!