The Visionary Amethyst:
It is in the Ice Caves. When the path ends there is a giant body of a downed golem. Search his head for the Amethyst.
Northern Tundra:
Go back to Arokh and mount. Fly up and you will see a cave entrance closeby.
It's the entrance you want for the Northern Tundra. You will come back here later. But right now you need to fly southeast.