North of Waimea on Kauai, the Waimea Canyon Trail mountain bike route starts just east of Waimea Town and heads north parallel to the Waimea River. It starts as an old dirt road crossing the river several times. It provided access to an old hydroelectric power generating station several miles upstream. Beyond the power plant, the mountain bike trail is much less used and eventually ends at a river crossing. The trail continues again about 0.25 miles upstream on the western bank, so you will have to do some rock hopping in the river to get to it. When the trail continues again, it is a narrow trail that is used by many hikers and backpackers. There are several reservation only camping site (they are not very clean). The northern most terminus provides access to the main falls in the canyon.
Here are some notes on adventuring in Hawaii. First, unlike mainland forests, the tropical island forests can grow very dense and can mask dropoffs. Plus, the trails can be very wet and slick most of the year (December to February is the main rainy season, but expect rain all year round). Stay on the trail to avoid disorientation. Second, speaking of disorientation, be aware that most Hawaiian topographic maps use the Old Hawaiian Datum. When trying to use the latitude/longitude from those maps with a GPS unit, you will think you are 0.4 miles south/southeast of where you really are. Kind of important in a dense jungle. Third, the bacteria Leptospirosis is found in the local waters and mud. It causes flu like symptoms within 2-20 days of contact, and can be fatal if not treated with antibiotics. Fourth, when hiking about, walking sticks can be very helpful for stablity in the slick conditions, for probing mud hole depths and clearing webs of the tiny crab spider.