Alright. In the Old Wayfarer's hideaway, you get the shovel. Go to the stone tablet with the woman in a yellow dress next to it complaining about it. Dig in front of the palm tree north of there. In the exposed cavern, you will find the only path through the fog. You must follow the path EXACTLY, or else you'll end up back at the edge of the fog. Once you get to the quadrent, you can search north and east of the Isle of Gust to find two different islands.
Bonus: If you go west from the northernmost island (the one you have to find), you can begin to see the mast of the Ghost Ship (and maybe catch a glimpse of it if you continue). Be warned, though. If you go after it, you'll end up at the edge of the fog.
Above and beyond, no?