I LOVE the Hilton Waikoloa! I've stayed there 3 times.
Here are some of my favorite places to eat:
Kamuela Provision Company (at the Hilton Waikoloa) - try the Kamuela beef:
http://www.hiltonwaikoloavillage.com/dining/kamuela-provision.asp
This is a higher end table service restaurant.
Cafe Pesto (Kawaihae, a short drive north of Waikoloa):
http://www.cafepesto.com/
Table service, very casual.
Merriman's (Waimea):
http://www.merrimanshawaii.com/
I'm not sure how it is during dinner, but at lunch, you can get away w/ wearing shorts here. It's not really high end, but maybe a little above casual.
Rainbow Cafe (Hawi - north shore of the Big Island) - try the lamb burger:
http://www.gokohala.com/business/dining/KohalaRainbowCafe.html
This is a counter service hole-in-the-wall across the King Kamehameha statue, but it's very good! A great place to stop if you're driving around.
I could seriously spend a week at Waikoloa without leaving -- check out the vendor by the pool or lagoon and see if they have any length-of-stay recreation specials. We were there once where we payed a flat fee and could use all of the kayaks, floats, waterbikes, etc., that we wanted during our stay.
I love the drive up to the north shore, Hawi, too. If you get all the way to the top, you can see wild horses and islands off the sheer cliffs. I think there's a hiking trail too, if that's your kind of thing.
If you have time to drive to Hilo, the drive up the Hamakua Coast is also beautiful. You can see Rainbow Falls and Akaka Falls there. If you go to Hilo, stop by the Big Island Candy Company and buy the chocolate covered shortbread cookies. Expensive, but awesome! They make great gifts for people at home too. They're chocolate mac nuts are also really good -- much better than the cheapy Mauna Loa mac nuts, but again, expensive.
There's a mac nut farm tour somewhere in the Hilo area too. And if you're in Hilo, there's Ken's Pancake House. It's a casual table service restaurant, with big portions, lots of choices, and good food.