Personally, and everyone has a different view, I would focus on the Big Island and Oahu.
I just find the Big Island amazing.... some many different climates... you can go from 80 degrees in Kona or Hilo to snow and freezing temperatures at Mauna Kea. The stargazing at night is amazing. Visit to Volcano National Park, Waipio Valley and other attractions are not to be missed. On the Big Island, you have to consider time in the car... things are spread out.
On Oahu, Pearl Harbor is the most popular site and not to be missed. Personally, I do not find much more there that you cannot find on the Big Island.
But, then again, I could be a Goodwill Ambassador for The Big Island!
No matter where you go in Hawaii, you are in for a treat!