Hiking
Waimea Canyon
Go for a hike. There are moderate ones like the Nounou Mt. Trail (less than two miles) which will take you to the chest of the "Sleeping Giant" landmark and 360 degree views. If you have more stamina, check out Waimea Canyon (it bears a resemblance to the Grand Canyon). The Kukui Trail is five miles round-trip, dropping 2,000 feet and offering the shortest route to the canyon floor (and a large swimming hole at the bottom as your reward). If you want the quintessential Kauai hiking experience, walk some of the Napali Coast Trail. Doing the whole thing is only for very experienced trekkers, but those in decent shape and with a sense of adventure who don't mind mud (and ripe fruit on the trail), will be rewarded with views of waterfalls and rainbows.
Discoveries on the Water
Napali coast by boat
Take a Zodiac boat ride. A Zodiac is a large rubber boat with a motor on it--yet it is small enough to maneuver into cool cave formations. If you are not up for hiking the Napali coastline, a Zodiac is a great way to see it.
Kauai is also a perfect place to go snorkeling. The beaches are smooth and the water is bathtub warm. Prior experience is not needed and you can rent a mask and fins on the island. Po'ipu Beach on the south side and Tunnels Reef on the north shore are both excellent snorkeling spots. Purchase a bag of frozen peas from a local grocery store to attract fish and bring along an underwater camera (disposable is fine) to snap their pictures when they swim up. Your photos will turn out best if you wait for the fish to swim into the sunbeams.
Scuba diving is also an option--head for the southern beaches where the water is calmer and visibility is up to 50 feet in the water. Some outfitters have an introductory scuba session for those who aren't certified. You can get certified while on the island but ask in advance what medical paperwork you need to bring.
Air Adventures
Helicopter tour view
Take a helicopter ride. Ninety percent of Kauai is inaccessible and if you don't have a fear of heights, this is the way to get a bird's eye view of the interior of Waimea Canyon, the ancient crater of Mt. Wai'ale'ale, dozens of waterfalls and once again, the Napali coast.
If a helicopter ride is too enclosed for you, then by all means, channel your inner Tarzan and opt for a zipline tour and coast over the treetops in a harness. Some of the zipline tours have combo packages and combine zipping with kayaking and swimming.
