The “Ann and her Sisters” side quest involves speaking to Ann aboard one of the Airships that travel between the various Aerodrome locations throughout Ivalice and then seeking out each of her sisters aboard each of the other Airships. It cannot be fully completed until you can reach every Aerodrome in the game - specifically, after you have reached the Balfonheim Port.
Travel to an Aerodrome and board one of the Airships. The first trip that you take can be between any two Aerodromes in Ivalice. Choose to travel “By Leisure Craft” which will allow you to explore the Airship during the journey (whereas “By Private Cabin” will just take you straight to the destination).
Take the doorway at the bottom of the staircase (directly behind the area where you first start off when aboard the Airship). Speak to the man named Rande and the woman named Ann on the bottom floor to initiate the side quest by selecting the “Who’s this… Rande?” option when prompted. Ann will give you an item called Ann’s Letter. Ann will ask you to seek out each of her sisters for her.
There are now seven flights that need to be taken – it does not matter which flight you took to first meet up with Ann originally. The flights are:
There is no way to make all the trips without having to backtrack at some point. Just use the “Travel by Private Cabin” option to speedily get to the last Aerodrome that you need.
Speak to the lady behind the counter during each of the trips. The flight that you first took to meet Ann will not have one of her sisters on it, but each other time it will be one of Ann’s sisters.
The last sister will give you a 
Ring of Renewal accessory as a reward for completing the quest.
The Ann’s Letter side quest is now completed. This quest is normally completed when you reach Balfonheim Port. Click on the link to return to that section of the walkthrough.
