Couple other suggestions - obviously do as much as you can, head over to Hilo, go up to Volcano Nat'l Park .. About a 3 mile hike from South Pointe is a green sand beach. The beaches in Kona are not bad, but if you really like Beaches with a capital B, drive 45 minutes north to the Kohala coast. You'll go through lava fields and you'll think you're on the moon
but they're worth it. In general a lot of stuff is off the beaten path so you have to explore a little.
Book a snorkel trip or kayak trip to the Captain Cook memorial. Bonus points if you can say the name in Hawaiian (Kealakekua Bay). Not only for the history, but it's a fantastic spot for snorkeling also. Wild dolphins will swim up nearby and you can hear whales too not too far off depending on the time of year.
There's a really neat Botanical Garden near Hilo. The Big Island is a little like other islands in that the west side is the hotter drier side and the east side is the wetter greener side.
If you like coffee .. if you think Kona coffee is good in general, you haven't seen anything yet. They seem to save the REALLY good stuff for themselves and sell off the dregs
Maybe not quite, maybe it's just the "being there makes it taste better" thing, who knows .. either way it's really good. There is a coffee plantation you can check out, on the grounds are some lava tubes you can hike through .. pretty keen stuff. What impressed me most about Kona's coffee is that it's a total cottage industry / co-op. People have coffee trees in their backyards and take the beans to a drop off point for processing. Whereas in Kauai the coffee was a total plantation style industry. Kauai coffee is good too (this tread IS about Kauai
)