Before unlock the vault, you won’t be able to open/find a chest that contain Gale Key!!! So, you may want to re-visit few areas again, if you can’t seem to find anything there before.
You can go to vault easily after that simply using vault on the town menu.
|#1||Lake Dorr||Sonic Knuckles|
|#2||Town of Kolts||Equip Hat|
|#3||Aquapolis Olderion||Recipe for Wyvern Feather|
|#4||Town of Amore||Tornado Ring|
|#5||Village of Ambel||Recipe for Mythril Plate|
|#7||Aquapolis Olderion||Blessed Hammer|
|#8||Ghost Ship||Golem’s Staff|
|#9||Industrial City Dilmagia||Recipe for Moon Bracer|
|#10||Mystic Woods||Recipe for Mythril Saber|
Obtaining all gale Key will rewards you with Air Knife (Dagger; Atk + 46 Wind Element)