Your objective is to find Fiore in Central Resulia. However, there are some optional tasks you can do before proceeding with the main story. There are new, stronger enemies roaming the other areas now so you can spend some time farming them to earn some extra EXP, SP, Fol, and items. The weapon merchants in Myiddok and Central Resulia will carry newer equipment as well but I suggest buying them from the capital instead.
These are rifts leading to anomalous locations in space and time. These portals appear at specific spots in different areas. Once you enter them, you can't leave unless you clear the area or your party gets wiped out within its halls. The enemies within each Cathedral is scaled to your level. At lower levels, you have to clear three rooms; as your you progress in the story further, you'll need to clear more rooms. In the last room of the Cathedral, you'll find a powerful corrupt called an Eyebalone. This monster is capable of dealing high amounts of damage while maintaining an equally high defense and HP. Careful preparation is needed here; you may even probably need to use your Reserve Rushes to defeat them.
After defeating the Eyebalone, you'll be able to loot the treasure chest near the exit. You can complete the same Cathedral as many times as you want; however, you can only loot the chest once. It's also okay to come back for the Cathedrals that may have appeared but your party have problems dealing with it at that point of time.
Make your preparations. When you’re ready to proceed with the story, exit the capital through the southwestern gate.