The things I enjoyed most while there was snorkeling in Kona, which included a night snorkel with Manta Rays. If you have an underwater camera, I would obviously recommend bringing it. If not, I would say considering getting the Nikon AW100 for the trip. For $200, it's well worth the investment and if you can convince the other members in the party to pitch-in for it, I'd go for it. Plus, the thing has HD Video, which is incredible when snorkeling.
If you're staying near the Kona side, the drive to Mauna Kea to see the active lava flow (which was restricted when I visited), is a good 6-7 hours. That's definitely a day trip! The visitors area on top of the volcano has a small viewing area of where you can see the glow from the lava. Definitely check with the visitors center before you drive over there if you can hike to see the active flow or not.
In the same area as Mauna Kea, the national park which it's located-- there's a great lava tube to see. You'll descend some easy rain forest (via paved walkways) to get to it. Very interested stuff! I have a great pano from inside, so I'd suggest bringing your tripod.
I lived in Maui when I went on this vacaiton, so my 'hiking' list was pretty much nonexistent. Visiting Big Island was a 'leisure/relaxing' trip for us, so sorry the list is a bit short!