A Hat For A Hat

 is the second quest given by the Innkeeper and the third quest in the Main Quest line.

Quest Dialogue
Beginning the quest:

Turning in the quest:

Walkthrough
To begin the quest, talk to the Innkeeper and choose Helping the Innkeeper. He will say that he'd like to get some revenge on the pirates that stole his hat, and steal one back from them. The Old Pirate's Hat you're looking for can only be found in Silver Pirate Chests on Battlemaster Settlements. These islands are quite far from the map's origin, but the Innkeeper can now give you directions to one. Simply ask Directions to... followed by Tough Pirates and he will direct you to the closest one.

Keep in mind that Silver Pirate Chest require a Silver Chest Key to open. If you do not have one, you may ask the Innkeeper to direct you to a Merchant that sells one. Pirate Battlemasters and Pirate Commanders also drops silver keys.

Once you've found the Old Pirate's Hat, return to any Innkeeper to turn in the quest.

Rewards

 * Explorer's Charm

Trivia

 * The Black Old Pirate Ship always contains a silver chest. It's possible to loot the hat from this chest.