At this point, you have completed about 50% of game. It's time for you to leave the Floating Continent; don't worry, you can always come back any time. So, what you need right now is to upgrade your Enterprise so that it can fly outside of the continent.
Since you've already collected all chests, just go straight inside and talk to the king. He will give you Wheel of Time and instruct you to visit Cid.
Go to Cid's house (1), enjoy a short backstory telling from Cid. After that, He will help you upgrade your ship.
Now that your ship is upgraded, you can fly to any direction to exit the continent.
