The big map will highlight the region boundary if you have a quest objective in an adjacent region. The bigger issue is when the region you need isn't adjacent to the one you're in. Go to your journal, select the quest, and use the "Map" button below the quest description. That will show you what region you need. Beyond that, while it is possible to follow the region boundaries on the maps to see how it connects to where you are, it's more a matter of learning the territory.

To get to the Central Shroud, you'd take the Blue Badger Gate to the southeast of New Gridania (near the Adventurer's Guild).
To get to the North Shroud, you'd take the Yellow Serpent Gate on the western edge of Old Gridania (near the Conjerer's Guild).
To get to the East Shroud, you'd take the ferry at the east side of Old Gridania (near the Lancer's Guild).

That'll get you through the first several levels, by which point you'll have had some time to get your bearings.