We led natural history trips to the islands, for Adult Education at the University of Nevada, LV for many years in the ol' days. We called our trips The Other Hawai'i. Folks would return from our trips, tell friends what they saw and their friends who knew the islands had never heard of most of the places we took folks. "What?," the friends would say, "You didn't see Waikiki? Or Pearl Harbor?" Of course, our purpose was to learn and teach about island geology and biology. We used to have native Hawai'ians join us with their kids - "we have learned more about our islands from you Nevadans than all our years on the islands."
One of our favorite places on Kauai for a glorious hike and beautiful views away from the tourists places: Koke'e State park. We would stay in their rustic cabins in the high country well away from most folks, surrounded by wild chickens and beautiful forest.
And our favorite hike in the Koke'e: Awa‘awapuhi Trail. The folks at the natural history museum (an excellent museum)will give you directions and current conditions.
The trail takes some energy since it descends steadily for about 1,500 feet. You walk through beautiful rain forest and then a dryland forest until reaching the scenic cliffs of the Na Pali, several thousand feet above the coast. The return is a steady uphill. The walk is on the sunny western slopes of Koke'e, so a morning start is suggested. Bring water, snacks and sunscreen. If you (or others with you) are strong hikers, you can make it a loop walk. Begin on the Nu‘alolo Trail (the steeper descent of the two), join the Awa'awapuhi to walk to the Pali and return uphill on the Awa'awapuhi. The Loop is somewhat over 10 miles and the back and forth Awa'awapuhi (our recommendation for most folks) is a little over 6 miles. After you return from the hike, be sure to get a piece of lilikoi pie at the food stand near the visitor center - it was always our reward.
Another great walk we used to lead folks along in Koke'e is the Alaka’i Trail, into the Alaka'i Swamp. One of the wettest spots in the US, great birds (some native rarities - like the Iiwi), and marvelous rain forest. Mostly on board walks, when we last did it.
Have a great trip.