You can do whatever you need to here, like use the Inn or Sanctum, or sell stuff. You can visit Briggs in jail for an amusing scene where you find out that Eoleo can use Psynergy. Oh dear. They seem to be hiding this from you, although the fact that the sea fighters that accompany Briggs, along with Briggs himself, can actually see Psynergy being used leaves a little to the imagination...
Anyway, when you're done here, go to Eastern Alhafra and the boat again. Remember the big rock? You can now use Burst on it to blow it to bits and free the mast. Chaucha and Eoleo as well as some workmen will notice the fact that it has disappeared, and so they'll run off. Now Briggs and the mayor of Alhafra know. This spells trouble.
Try to leave, and the mayor of Alhafra will show up. You'll be invited back to the manor, and you'll have a little discussion. A rather disturbing silent scene will occur, and then a soldier will appear. Briggs has escaped! Once you've regained control, go back to the boat, and watch the scene as Briggs escapes on it.
Despite what you may think, you can repay the Mayor's favour. By stealing more of his stuff. Go back to the cave (the man guarding it is out of the way again) and you can go inside. Go down the ladder and all the way down until you emerge inside Briggs' cell. The jar on the right-hand side contains some Power Bread. Go back up to the puddle, freeze it, then go back up to the ladder. Hop around and across the bridges to the right, then you can use the ice as a pillar to hop across. Raid the chests for 777 coins, a Potion, and a Psy Crystal, then leave the cave.
Use the Inn or whatever you need to, then leave Alhafra. Use your own boat to head all the way north to the beaches on the southeastern coast of Angara. Get off on the big one and head north to enter Champa.