Once you've escaped Barhiem Passage the option of Leisure Craft opens up when going by airship. On your first Leisure flight track down the Chief Steward. She should be in heated conversation with a guy named Rande. Continue prompting conversation with Ann until you agree to deliver letters to her sisters to help get them free of their persistent marriage suiters. YOu then get Ann's Letter.

With that letter you must track down all seven of Ann's sisters who are all Chief Stewards on seven leisure ships. You must make seven flight paths on the following routes:

You don't have to worry about order, you simply have to deliver a letter on all seven of the above routes. When you've delivered the final letter Vaan will receive a Ring of Renewal.