Rogue Galaxy Quarry: Ancient Fairy
The closest save teleporter to take in order to reach The Ancient Fairy is Leo King's Castle - Entrance. He is located in the very first circular room you come across here, pretty much impossible to miss his location. Unlike the other Quarries in Rogue Galaxy, The Ancient Fairy requires a weapon to summon, Zipangu Axe. If you're without this item you can purchase it from the shop in Burkaqua Village.
None of the quarries in Rogue Galaxy consume the item required to summon them. That's why I recommend you try and keep at least one of all items that are required in the Revelation Flow on you. Some of the quarries require items not used in the Revelation flow which are usually acquired by some other means on the same planet as the quarry. More information for those quarries are found in their select guides.
The Item to summon the Ancient Fairy is a Zipangu Axe. The Zipangu Axe can be purchased from the guy who runs the shop in Burkaqua if you don't have one. It is a weapon for Deego, as seen in the picture above.