If you're on the hunt for the southernmost place in Croatia, set your sights on the Prevlaka peninsula. Roughly 50 km southeast of Dubrovnik, this strategic little plot of land is located at the mouth of Kotor Bay. So tactfully advantageous is it, in fact, that the Austrians decided to construct a fortress here back in the 19th century, appropriately dubbed either "Prevlaka Fortress" or "Fort Ostro" (the latter for the point on which the stronghold stands).
If you're feeling culturally inclined, make the hour-long journey from Dubrovnik and then either rent a bike or follow the trail out onto Cape Ostro. Not only will the natural scenery impress you, but you'll also have the opportunity to get a first-hand look inside the massive (however worse-for-wear) fortress. And the fact that you'll likely have the peninsula seemingly to yourself? Just consider that a peripheral reward for venturing away from the "Pearl of the Adriatic". Well played.