After the scenes aboard the ship, use the Save Sphere and follow the people into the remains of Kilika. At the bar, head west and you’ll find Yuna to watch the "sending". You’ll find out more about that in the scene itself, but, anyhow… You’ll awaken the next morning in the inn. Use the Save Sphere if desired, go outside and speak with Wakka to the east. Head into the local tavern at the "Y" fork for the Al Bhed Primer Vol. IV as well.
Along the southern part of the village is a weapon shop. Meanwhile, if you head west of the tavern, you can find a destroyed house with a girl in the ruins; save her, then go to the tavern again for an Ether chest. Continue west from the tavern along into the Woods, grabbing three Potions from the last house before reaching the woods.