...then Big Island is one not to miss. Just for VNP, fly into Hilo as its the closest airport, but I would recommend 4 or 5 days there minimum and do the Island drive and explore. When spending a bit more time, it maybe easier to get a flight to and from Kona. There is black and green sand beach, south point, Mauna Kea, Waimea Canyon, Kona Coast.. You could spend a week exploring VNP.
Plus Big Island has the best cuisine of any of the Islands. Mauna Kea (luau, Sunday Brunch, Clambake) simply outstanding, Four Seasons Hualalai Beach Tree, Prince (Lets go crabbing), Merrimans in Waimea, and not to mention the award winning Blue Dragon.
While I agree with some of attractions to be seen -- except for South Point (and I'm not sure why the previous poster would suggest Waimea Canyon since it's not on the Big Island
) -- I would also note that none of those restaurants recommended will give you the slightest flavor (pun intended) of what truly local food is like -- particularly if you need to give some attention to budget realities. The same is true on any of the islands (although I know the Big Island much better than the others): you can eat amazingly well and in truly local style for 1/8 the cost of Kohala resort restaurants if you do a little digging and talk with folks who actually live or have lived there and don't just do "shore tourism."
ETA:
Given your thread-opener, and the advice of posters upstream, let me call your attention to these threads, if you haven't already seen them:
http://www.flyertalk.com/forum/hawai...t=consolidated
http://www.flyertalk.com/forum/hawai...t=consolidated
http://www.flyertalk.com/forum/hawai...t=consolidated
http://www.flyertalk.com/forum/hawai...t=consolidated
http://www.flyertalk.com/forum/hawai...t=consolidated
http://www.flyertalk.com/forum/hawai...t=consolidated
http://www.flyertalk.com/forum/hawai...t=consolidated
http://www.flyertalk.com/forum/hawai...t=consolidated
http://www.flyertalk.com/forum/hawai...t=consolidated
http://www.flyertalk.com/forum/hawai...t=consolidated
http://www.flyertalk.com/forum/hawai...t=consolidated