As with most islands, if you drive far enough you're likely to find the end of the road. Kauai's Na Pali Coast is far too rugged (and beautiful) to permit a road completing the circumnavigation of the island.
This is where the northern road comes to an end: Ke'e Beach.
It's a spectacular place, and a beautiful beach. Hiking trails take you up into the shear cliffs of the Na Pali.
Now...if you can only find a parking place.
(Sorry, that's a joke only the people who have been to Ke'e will understand. You drive for miles through what seems to be a very isolated road, ending up in a parking area packed - i mean packed - with cars. The trick is to get there very, very early.)