I was there a few years ago. Will go back when the kids are older, as it is an awesome island for outdoor activities.
I found the beaches to be lacking compared to a Maui or Oahu. Most of the good ones have a hotel on them as the only access point (at least that was the case in the NW Waikoloa area). However, there is a law in Hawii that each beach regardless if a hotel is the only access point must have public parking and access. So drive up to the hotels and ask at the gate for a beach pass. Mauna Kea Beach is quite nice, and you can get passes at the gate.
Waimea has an awesome farmers market. Everything is grown local. We bought Vegetables, Fruit, even Tea that a local grows there. The eco-system allows for virtually anything to be grown.
If you are a diver, do a night manta ray dive. We did ours down by the airport. Just amazing as it is you and these massive manta rays coming out of the dark mouth wide open to feed.
Other than that there is a food place I did not try that is #1 in the world on yelp in Kona. It is called Da Poke Shack, Kailua-Kona, HI. Try it and let me know!
EDIT: Oh and there is this locally (Big Island) made Macadamia Ice Cream I bought at ABC store, get it. It is hands down best ice cream I have had anywhere. Oh and there is a coffee tour that is really good:
http://www.huladaddy.com/. Kona coffee is a must when your there.