Not far to the northwest of Naples, high above an inhospitable stretch of coastline facing the depths of the Tyrrhenian Sea, there is a bare patch of ground whose powdery surface is marked by the gaping entrance to what appears to be an ordinary cavern. Many casual visitors arriving at this spot today would never suspect that two thousand years ago, and for quite a long time before then, this unprepossessing opening in the rocky soil had been renowned all over the Mediterranean...
I have physically been to this location an desire to nitpick.
1) The location described here appears to be the GROTTO of the Sibyl, not the Cave of the Sibyl. The Cave of Sibyl is very clearly manmade, albeit anciently so.
2) Which is important, because the Grotto is just an ancient escape tunnel from the city.
3) In order to "miss" the actual Cave of the Sibyl, you'd have to miss the sole walkway in the area leading directly to it and the giant plaque explaining exactly what it is.
4) And the reason it has a powdery surface? THEY USED DYNAMITE to uncover it in the first place. Also it's a part of a manmade pathway.
5) And while we're on the subject, archaeologists don't consider the "real" cave of Sibyl the true cave either (it's probably just a Greek defense tunnel from the time the town was a Greek colony.)
6) Neither location is "high above the coastline." In fact, both are far below the city ruins itself. The coastline is farther away from the location now then it was during the Roman Republic/Empire because of the volcanic nature of the land shifting, and likely would have been right next to the town harbor in ancient times.