The Big Island all the way.
Where else can you walk up to lava? I highly recommend Kalapana Cultural Tours for a chance to get up close and personal with the lava. As long as it is flowing onto the private land when you visit they will let you walk close enough to touch the lava.
http://www.kalapanaculturaltours.com/Lava.html
And what about driving to 14,000 feet and seeing some snow and an amazing view? This one is not really recommended for younger kids but we did it anyway. We made sure to spend several hours at the visitor center at 9,200 feet to give everyone time to acclimate before driving to the summit. We packed a picnic dinner and spent some time looking through the telescopes that others had brought. Then drove to the summit, the road is gravel and in good shape. We were in a virtually brand new Toyota 4 Runner that had no issues with the drive up or down. Both were done in 4 wheel low and down in particular was me just steering. No breaks or gas were required. There was another couple up there in a sedan of some sort. By the time they reached the top they had to open the hood and let the engine steam and cool off. We stayed to watch the sunset and then for another couple hours while my wife took some pictures of the night sky.
http://www.ifa.hawaii.edu/info/vis/visiting-mauna-kea/visiting-the-summit.html
We did both with our kids at about those ages, certainly not the safest vacation and it did require a visit with my sons science teacher the next year because she thought he was lying about walking right up to flowing lava and was upset he wouldn't admit it was lying. A few pictures cleared up the misunderstanding.
As for a resort we always have stayed on the Kona side at the Sheraton at Keauhou Bay. There is no beach there but we really love the view and the location.
One thing to remember is you do A LOT of driving when staying on the Big Island. The places to see and do are all FAR apart.
Here are some pictures from our first trip to the Big Island. I don't think we ever uploaded any pictures from the second trip when we visited the summit of Mauna Kea.
http://www.judydonnelly.com/Travel/Destinations/Hawaii1/Big-Island/