When you exit the Silver Ruins, you come out in the Arctic Region. There are 3 buildings in here.
The first one is the Arctic Plateau, which is basically just an Inn and an Item Shop.
There are no treasures in the Arctic Plateau, but the Item Shop does have some insanely expensive accessories (which you really only need if you're going for a 100% completionist game).
To the southwest is the Arctic Base Remains, and then in the center of the world map is the Tower of Mirrors.
After resting/saving at the Inn, your next destination is the Arctic Base Remains.