As this is a side quest that can be pretty annoying and really boring(there can go a lot of time to find all the sisters) i wrote how to do it here fast and easy:
- Go to any aerodrome and board a ship by leisure option (I began from Nalbina to Rabanastre). Once aboard, go to the Sky Saloon and talk to Chief Steward. Choose "Who's this...Rande?" to get some scoop and obtain Ann's Letter. One down, six to go.
- Here are the possible 7 routes you can take, equaling 7 sisters - you must talk to Chief Steward on each of these flights and show her the letter. They go in order Ann, Liddy, Twarra, Carryl, Sanne, Lyseth, Cisset. Once 7th sister is located, you get Ring of Renewal.

Nalbina to Rabanastre
Balfonheim to Archades
Balfonheim to Nalbina
Bhujerba to Balfonheim
Bhujerba to Rabanastre
Archades to Nalbina
Archades to Rabanastre