If you have any interest in science, be sure to take the guided tours of the Mauna Kea summit. They are offered on Saturday and Sunday afternoons. You show up at the visitor's center (just below 10,000') and caravan in your own vehicle to the summit (4WD required). In addition to seeing the incredible views at the top that you can see anytime by driving up their yourself, you also get a guide, and get access inside a couple of the telescope facilities that you otherwise wouldn't have access to. Dress warmly for winter weather - there was still snow on the ground when I went there in May. It makes for an excellent contrast to the other things you'll do on the Big Island.