i'll try to keep this spoiler free...

Eldbeak Peninsula is on the Trabia continent north of Balamb, extending south from the western half of the continent. Minde Isle (you'll see) is a featureless, mid-sized island south of the Esthar region.

The mountain with lake and cavern is northwest of Timber. You need the Ragnarok to find the stone. Look for a river that stops at a small waterfall in the plateau near some railroads.