There is a trail from the Mauna Kea Onizuka visitor center (9000ft) to the summit. Near the top the trail ends and you finish on the observatory road. Round trip half a day to a whole day depending upon whether you walk down or hitch a ride back to the visitor center.
Hiking from the ocean sounds interesting, but the distances are great. Via Onizuka vistor center, the shortest distance would be from the East, from Hilo, I am guessing about 30 miles. You may need to hike along the Saddle Road as much of the land in Hawaii is private (huge ranches) and near wear the access road to Onizuka visitor center leaves the Saddle Road there is an artillary range.