When you gain control over Zidane again, head up through the streets and into the next area. Search the rubble next to the house when a ‘!’ appears to get a Lindblum Card. Go into the house to the right and open the two chests for a Phoenix Pinion and an Ether. Leave the house and move to the left and exit this screen. Minister Artania will take you to see Regent Cid. Read all of the storyline and once Regent Cid is finished talking he will give you 3000 Gil.
Now you will have some time to further explore the remains of the city. You can buy some healing items from the woman standing in the middle of the burnt down building at the top of the screen. You can also buy some new equipment from the shop located in the middle right of this area. Make sure to buy the Stardust Rod for Dagger if you missed the chance to steal it from Zorn back in Alexandria. You can visit the Synthesis shop that is found at the top left corner of the screen. I suggest forging the Exploda because Zidane is probably in need of a new weapon.
You can also visit the Inn if you would like, you can talk to the Moogle named Moodon and he has a letter for you. Now go into the aircab terminal and take the cab to the Theater District, go into the house by the bottom of the screen and open the chest for an Ore. Go through the area and exit through the bottom left of the screen. Move into the house to the left, open the various chests scattered around the house to get 340 Gil, 993 Gil, and 262 Gil. When you are ready go back and talk to the man in the Business District and tell him that you are ready.
You now have to head to the Outer Continent by passing through Fossil Roo. When you reach the base level you will receive a World Map from Regent Cid. You can save your game by talking to Moonte and you can buy items from the man standing here. Before heading out search to the right of the doors to find a chest containing a Bandana.