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-- Cave of Spirits --
Go to Gnome's cave (I suggest running from Doom Gaze), and go to the room where you flipped the switch that started the alarm. Go in the leftmost door for a chest (Emerald Ring).
-- Long Valley --
Go into the cave of the Long Valley, into the room that was filled with Shoki (go down the rope in the hole at the far right of the cave). Follow the path and you'll see a chest (Reverse Doll). From there, go down, left, and up above the bubbling pool for another chest (Amethyst Ring). Go back to where you got the first chest, then go right and up to where there's another bubbling pool. Go down from the pool for a chest (White Mist). Go back up to the pool, then right and down for another chest (Iron Boots).
-- Undine's Cave --
Undine's Cave is north of Venezzia. If the pool in the first room is empty, go through the north door, right and down and flip the switch.
Otherwise go right, follow the path, down the stairs, down and left across the bridge, and down and don't flip the switch.
Go up and through the door, then follow the path through the door. Go up into the room where you fought Undine, and to the top of the room for a chest ([spell] Ice Wall). If the right-hand pool in the last room was full, flip the switch above where the chest was in this room. Then go back out and go down the steps in the right-hand pool for a chest (Sapphire Ring).
-- Demitel's Island --
Demitel's Island is southwest of Venezzia. Go to the chamber where you fought Demitel for a chest ([spell] Death Cloud).
-- Thor --
In Thor (northeast of Venezzia), now you can go into the door that was rusted shut before, where you can learn a little more about the civilization of Thor if you sit in front of the counter...
Set Arche to cast Indignation, and Klarth to cast Volt. Go to the Mother Computer and ask about Aska.
-- Cave of Darkness --
NOTE: You have to have gotten the Amethyst Ring from the Long Valley for there to be anyone in the cave. Northeast of Thor, the continent where it's always dark has a cave southeast of the city. Go there.