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I don't believe you will encounter any in hidden chests until you reach Saronia Castle, which is a little ways away (not too far). You will have to complete the Sewers, Goldor Manor, and the Goldor boss fight before your ship is unlocked (by obtaining the key from defeating Goldor).
After which you may travel Northeast to Saronia Castle and there are 2 Phoenix Downs. Also the Northeastern village of Saronia has the "Raise" spell for anyone who can access Level 5 magic. This will illiminate your need for Phoenix Downs.
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