This Materia cave is located in the mountains on the Wutai Continent.
You can reach this one with a Green, Black or Gold Chocobo.
With the Green/Black Chocobo, land the Highwind on the small grass patch on the west-most part of the continent and follow the mountains east to the cave.
With the Gold Chocobo, you can just run here from wherever you want.
Inside the cave is a Mime Materia.
This Materia cave is located north-east of Mideel.
You can reach this one with a Blue, Black or Gold Chocobo.
With the Blue Chocobo, land the Highwind on the small grass area south-east of the Temple of the Ancients and using the shallow water and the beaches you can reach the cave.
With the Black Chocobo, you can land on the grass by Mideel and run down the small cliff and along the rocky path.
With the Gold Chocobo, you can just run here from wherever you want.
Inside the cave is a Quadra Magic Materia.
This Materia cave is located North of the Corel Reactor path, North-East of North Corel.
You can reach this one with either a Black or Gold Chocobo.
With the Black Chocobo, land the Highwind by the Corel Reactor path and head north, over the deep river and across the rocky land.
With the Gold Chocobo, you can just run here from anywhere you want.
Inside the cave is a HP<>MP Materia.
This Materia cave is located in the North-East most part of the map and is not shown on the in-game map.
It can only be reached by Gold Chocobo, so start from the nearest land and just run there.
Inside the cave is a Knights of the Round Materia.