Mideel is your next destination. It lies on an island just south of the Junon continent. You can buy some really cool stuff here, like Crystal Bangles and Crystal Weapons. If you have some Samolen Greens, you can talk to the little chocobo that follows the crazy woman around. Choose to feed him the greens, then scratch behind his ears. He'll do a little dance, and then give you the Contain materia. Also in the Weapon Shop is a door that doesn't seem to open. Go out and up to the left-hand landing. Just behind the guy standing there, you'll hear a clink. Look, and find the Useless Old Key. Try and use it in the door. You'll discover that it isn't a real door. The owner will aplogize for the ruse, and give you some Curse Rings to make up for the loss of your key. Unlike the cursed stuff in FF3, you can't get anything better from it--actually, it raises your stats an awful lot, and the only bad thing is that it gives you the Death Sentence condition. That shouldn't be a be problem, because your stats will be high enough to end most battles fairly quickly. Just be sure to unequip it before a boss.
When you're done, head straight up the middle of town, where a scene will start. You'll find Cloud, but he's in no condition to help you. Since there's nothing you can do about his condition, head back to the Highwind. There, you'll learn about what's going to be done with the Huge Materia. Cid will be appointed the new leader, and the quest to find the Huge Materia will begin.