Situated on the northwestern coastline of the island of Kauai is the Na Pali (High Cliff) Coast State Park. The park consists of 6,175 acres of some of the most beautiful and rugged coast line Hawaii has to offer. The tall mountain sides make for narrow valleys and majestic waterfalls that carve steep 4,000 ft cliffs leading to the ocean. Extensive stone walled terraces can still be found at the valley bottoms where ancient Hawaiians once lived while cultivating Kalo (Taro).
The Kalalau Trail was created in the 1800's, with some areas being rebuilt in the 1930's and still maintained today. While only being 11 miles long, the trail is not recommended for inexperienced hikers. The first couple of miles make for a great day hike. If you're planning to complete the full trail, you will want to get a camping permit at either Kalalau or Hanakoa camp sites. Here is the DLNR site, for more information.
If hiking is not your cup of tea, you can also tour the area by boat, or my personal recommendation: helicopter.