Many people say the west side of Kauai is the most scenic place on earth. If you can muster a 6.5-mile rugged roundtrip hike on the Awa'awapuhi Trail your destination is the backside of the Na Pali coast where lush green, eroded cliffs stand at ocean's end. Sight-seeing helicoptors occasionaly buzz overhead, but quickly leave as hikers have their own private up-close view that is worth more than any helicopter ride. Stay long enough and you could spot mountain goats or a rainbow. This scenic place wouldn't be green if it didn't rain a lot, so bring a poncho and protect your camera. The trail is often very muddy. You will want hiking shoes. Be careful as you go downhill on the way to the lookout.
If you want even more tranquility, drive to Polihale Beach on the far west side of Kauai. There are miles of the best sand in Kauai, plus dry weather is always in the forecast. Swimming isn't recommended however, as the waves are usually rough here. It takes awhile to reach Polihale as the unimproved road is in horrible shape. Expect to drive slowly another 30-45 minutes once the blacktop ends. Once there, you need only share the many miles of beach with just a handful of visitors.
The most popular scenic place on the west side of Kauai is Waimea Canyon. It is about an hour drive west from Lihue depending on the traffic. Many say it is more colorful than the Grand Canyon since more greenery blends with the colorful rock layers. There are several outstanding lookouts on the drive up, as well as great hiking trails.