Once you have gained control over Vivi, there are a few things to do in Alexandria. Head to the right, you can play an optional mini-game here by talking with the Hippo lady, agree to race against her son Hippaul to begin. The game is very simple, just press the 'Square' and 'Circle' buttons rapidly. Each time you race Hippaul he becomes better. As you race him enough and his level goes up his mother will give you items. You can check out which items can be won by looking in the "Side Quests" section of this guide. Once you receive the Athlete Queen key items there isn't any reason to continue racing him.
You can win some rare cards from this mini-game, so unless you are into the card game this isn't really important. This is your only chance to play this mini-game so play it while you can. Once you are done head back to the last screen and move all the way to the town square. Move into the alley, pass Blank and Marcus for now and head into the bell tower. Climb the ladder and ring the bell once you have reached the top, you will find the Shiva and Ramuh cards. Head back down and talk to Stiltzkin, buy his combo so he can continue his journey and talk to Kupo to save your game. You probably also have a letter for Kupo, he also received a letter delivered by Artemicion.
Now is the time to go back and talk to Blank and Marcus. When you are sure that you are finished exploring agree to see the play with them. You can go back to the square and purchase new equipment and stock up on healing items. The Synthesis shop is open, you can synth the new weapon Angel Bless for Zidane and you can also synth some other useful items. Once you have spoken with Marcus and Blank you will be taken into Ruby's theater to watch the show.
Doctor Tot will give Dagger an Opal, a Topaz, and an Amethyst. Once you gain control of Eiko, attempt to travel out of the castle. Your view eventually switches back to Zidane, head out of the pub and head towards the castle. You can go into Ruby's theater, search by the table to find 2680 Gil on the floor. You can head back to the bell tower and talk to Kupo, Stiltzkin left him a letter that you can read. You can buy Remedies and Hi-Potions from the item shop, now is a good time to stock up on them. When you are ready go back to the town square and move up to the castle.
After the short scene is over Freya and Amarant will join your party. Search by the platform to the left to find a Phoenix Pinion. Search by the one to the right to obtain 3927 Gil. When you are done approach the boat and head to the castle. Search behind the fountain for a Lapis Lazuli, go to the area to the left and head into the room. Go through the door to the left, which was previously inaccessible and search the top right corner for the Leo Stellazzio. Leave this room and head towards the entrance to the castle.
A sequence of events will take place and eventually the party will decide to go to Treno.