Mary King's Close: marked in yellow on this map from the Bank of Scotland's Museum on the Mound, which shows the current street plan in red laid over the 17th century plan in black. The construction of the City Chambers and Cockburn Street were the primary culprits in the close's destruction.
Modern view; Red line attempting to mark Mary King's Close as it would have gone.
That which we now call Mary King's Close seems to have begun its life as Towris (or Touris) Close, named for a property owner of the early 16th century. Later it became known as Alexander King's Close, then Mary King's Close. It is usually assumed that Mary King was the daughter of Alexander King, though it appears this cannot be definitively proven. In 1635, Mary King was listed as a tenant but not a landowner in the close, and the land in the close belonging to the descendants of Alexander King was described as "an empty wasteland" in the tax records, with no one living there.
Detailed depictions of Edinburgh's streets pre-19th century are hard to come by. The above is a map from the time of Mary King, though not very well detailed nor accurately scaled. Still, it helps us understand the lay of the land: Mary King's is approximately located in the red circle across from St. Giles (though the map does not correctly portray the number of blocks nor the number of buildings in the city.) The modern Prince's Street Gardens and Waverly Station sit in a hole that was once the Nor' Loch. The town of Edinburgh was almost entirely placed on top of a hill, and with sanitation being as it was in those days, it was convenient to just let the streets slope down toward the Loch so that the sewage and garbage thrown into the roads could naturally drain that direction.
Mary King's on a 17th century map. Stewart's Close is the zig-zaggy one to the right.
While other nearby closes tended to be cut off by buildings or would open out into nice airy gardens, the end of Mary King's Close, during the 17th century, went as near to the Nor' Loch as the streets could get, landing at the lowest part of the hill. It seems it was an important thoroughfare for this reason. Various 18th and 19th century construction projects have trimmed the close much shorter than its peak length, but the red arrow below depicts my understanding of how the close used to extend as laid over a modern area map. Fittingly, it seems it would have terminated somewhere around the modern Edinburgh Dungeon!
The "haunted" part of the close was said to be the portion after the modern Cockburn Street and going towards Waverly. It would have been the area nearest the Loch.
A small, fenced gap between buildings on Market Street which is now but a bricked up sliver, was for a while the final remnant of the haunted segment of Mary King's. The fence for some reason remains, even though there's nothing to pass into now.
Compare this picture of Mary King's old passage to the opening of nearby Craig's Close, which contains a narrow stairway leading up to the next street.
The Hebrides Bar has a little window out the back through which I tried to get what pictures I could. I possibly saw some remnants of stairs coming off from the old close. (The red and yellow circles over the maybe-steps, are a reflection on the window glass.)
Up on the High Street, the actual factual entry into the close is quite gone and has been for some time -- its High Street close-head was lost in the 18th century and by 1817 Mary King's was no longer considered part of the area (though most of the addresses in the "Exchange" Close had previously been Mary King's.) However, this photo below shows where the original entry would have previously stood, and it is also the plot of land under which the remnants of Mary King's Close are still preserved today.
The portion of Mary King's which ran after the City Chambers or Exchange still persisted as a busy street for about another century despite the loss of the High Street entry, at least until the interference of further construction brought its useful life to an end.
Mary King's is still clearly marked, but is entered by way of the Exchange.