Hello!
I'm actually on Adamantoise myself. As you progress through the MSQ, you will unlock more dungeons.
Keep an eye out for quest markers above peoples heads that blue with a + next to it, as those side quests can sometimes unlock dungeons as well.
If you have any questions during gameplay, feel free to add me, and you are free to message me within the game when i'm on!(ign is Lydell Aria)