When you enter Breezan Valley, get the treasure on the first screen then take the exit in the north. In this room, you discover that there are plants releasing toxic gas into the cave, and you can't go any further until you can nullify the gas. So, after the dialogue, exit Breezan Valley and go to Mosso Village.
All you need to do here is speak to the Male Outworlder in the inn (the one with the feathered cap).
The Outworlder (Tereno) will ask you to collect Optalir Grass from Stelumbra Cave and Tuphlos Flower from Hushet Ruins. After the dialogue, Stelumbra Cave - Other Entrance, and Hushet Ruins - Other Entrance will be added to the World Map.
Go outside, and you'll run into Jolie Curie. She gives you a Storage Key, and unlocks the "Stand" feature on your Magic Tablet. The Stand feature lets you place a buddy on a "stand" in your Secret House (if you're using a Planter and a Door, then you'll have to unlock a third room to place the Stand, but in my opinion it's totally worth it.)
When you place a buddy on the stand, it'll bring up your buddy list. In the bottom left corner there's a "Skill List" for each buddy. When you place that buddy on the stand, their "Skill List" will be automatically applied in battle (for example, Slime's skill is "Damage received 5% down," so if you put Slime on a stand, your party will receive 5% less damage in every battle.)
Anyway, now you need to go to Stelumbra Cave - Other Entrance, and Hushet Ruins - Other Entrance, both in the Rizolt Region. (And don't worry, I'll cover Mosso Village as soon as we're done with Breezan Valley.)