The Well House Tavern
It's housed in a building believed to have been constructed in the 14th century, though the Roman well in the basement predates that estimate. The tavern is said to be haunted - though the ghost, who wears a flowing white dress and is affectionately called Alice, is said to be good-spirited when she appears.
There is an acutal human skeleton in the basement of this place. Dating back to the 17th Century - said to be a plague victim.
The tavern is part of the Royal Clarence Hotel, Englands first hotel, said to be built on the site of Walter Raleighs fathers house - and apparently has a coughing ghost.
The pub is on the Exeter ghost/legends walk as either the start of finish point. And is built on part of the cathderal graveyard.