This from a friend in the know…
On the Big Island, we really liked the west coast area around Kona. It’s very different from anything else I have ever seen: black sand beaches, lots of black lava rocks, etc. You can see the place where Captain Cook was killed, too. Hilo is a dump, in my view. Rainy and bad hotel options. The national park is cool, and there is a good chance you will see lava flowing. We felt we pretty much saw the park in one full day. We are big Maui people. It’s our favorite island.
In Honolulu, I would recommend the royal palace. Jackie and I both toured it and found it very interesting. It’s basically in downtown. The area where you are staying in Honolulu will be busy and crowded, but also fun. We like a restaurant called Duke’s that’s right on the strip. Basic food at reasonable prices, and a good salad bar. Climbing up to the top of Diamond Head in Honolulu is also fun, and not that hard. We really like a place called the Side Street Inn in Honolulu. Great, local asian food that only the locals know about. It’s in a bit of a spotty neighborhood, but very good food. Go early, so you have a better chance of getting a table. If you want to see the apartment where Obama grew up, it’s pretty easily found, too. Just a couple miles from where you will be staying.
The island hops on Hawaiian Airlines are really easy and usually on schedule, if that’s how you are getting between places.