The end of the road on Kauai's north shore is the beginning of Napali (The Cliffs), which can only be accessed on land via the Kalalau Trail—an 11-mile squiggley scramble that ends in the Kalalau Valley. Don't even think about trying to dayhike the 22-mile roundtrip, since rough conditions make it seem more like 40 miles. On a busy day, nearly 500 souls set foot on the Kalalau, quite a circus, and second only in popularity to the Diamond Head Crater trail on Oahu. (A permit is required to walk beyond the first two miles of the trail.)
Make sure to pick a dry day, since rain makes this route the bad kind of adventure. It's also a good idea to show up early, if you want a nature trip rather than a social scene. Stuff your daypack with plenty of food and water. Wear sturdy shoes, and plan on getting them wet and muddy. A hiking pole will be a godsend.
Hanakapiai Beach is two miles in, though this is a rocky, dangerous swimming beach, and requires a stream crossing to reach. Flash floods can make for a lethal crossing, so much so that a million-dollar footbridge is being planned. Ribbony Hanakapiai Falls (above) is another two miles inland from the beach (so, 8 miles round-trip from the trailhead; no permit needed) and requires several more stream crossings. The hike to the falls will feel like 12 miles, so be ready.
You can achieve a great view of the Napali Coast by walking in about a half mile on the trail. The easiest way to see the coast is to walk about a hundred yards to the right at Ke'e Beach, which is also at the end of the road. Only a few, if that, visitors among the daily 500 people take one of the best hikes here, which is to follow a coastal trail around the point and then up to the ancient hula temple, the birthplace of the tradition in Hawaii. The hula temple is sacred ground in Hawaii, so treat it like a church. Another nearby attraction that is a totally five stars is Limahuli Garden (less than a mile before the end of the road). This place is Eden on earth. Complete directions for all these hikes are in the Kauai Trailblazer guidebook, now in its 20th year of publication.
For more remarkable long-distance hiking trails in the United States click here: http://bootbomb.com/info/hiking-trails/top-50-long-distance-hiking-trails-usa