You've typed a mouthful here: "A luau, the Arizona, volcano, Road to Hanna etc." That's three different islands. Setting aside the expense, each time you change islands you lose the better part of a day - packing up, checking out of the hotel/resort, turning in a rental car, getting to the airport, going through security, waiting for and then taking the interisland flight, claiming baggage on the other side, getting another rental car, driving to and checking into another resort/hotel -- you can see the time it takes to do all that. Depending on how long you plan to spend in Hawaii, and how much driving you're willing to do, you may want to do some research, and decide exactly where/how you will spend your time. A day trip to another island can be a huge time and money expense, for limited return on the investment.
I love Hawaii, and visit there often. I'm going back again this Spring. But it takes planning and effort to make the most of what you'll want to do with your time, and you can easily waste your vacation dollar if you aren't aware of your options. There is no way to see everything in one trip, and the best you can do is learn what is available and where, and make smart choices.
Now, here's what people will not tell you: Weather can be a great equalizer. If you live in a cold climate, yes, the Hawaii weather in December will most likely be nicer than your home state. But December in Hawaii can also be windy and rainy as much, or more than, it may be sunny. Daytime temps may be warm (mid-70s on a good day), but it can also be stormy and downright cold. A bored 17 year old may not have a very good time if he's forced to stay indoors on those days.
Surfing in Winter in Hawaii can be very dangerous. The big waves on the North Shore of Oahu can be well above the skill level of even very good surfers, and if your grandson isn't a great surfer, I'd rule those beaches out. Fun to watch the waves, but not safe to go in the water. (I've seen 40-foot waves at Waimea Bay in December. Incredible surf, but treacherous.) The South Shores of Oahu, (Ala Moana, Waikiki, Diamond Head Cliffs, Sandy Beach, and around to the south end of the Windward side, (Makapu'u, Waimanalo, even Lanikai or Kailua Beach), can be great beaches at that time of year, and they can easily occupy the recreational surfer. Waves up to six feet are common on the south beaches in winter, most days likely something lower, but fun for your grandson at any height. He's bound to find plenty of surf to occupy his time. Water temperatures will be cooler than in Summer, and will feel even colder if it's a rainy, stormy day.
The Polynesian Cultural Center offers an educational experience into the lives of South Pacific Islanders, but it can be expensive, and of limited value if you don't plan your day. The Park doesn't open till Noon, and it closes at 5:00, so they can start getting ready for the Luau and evening show. In that five hours you have to plan every minute, or you'll miss the demonstrations they perform at each of the seven villages. It isn't so much a casual place to walk around, if you want to get the most from the experience. I agree with others, that the luau food isn't all that great. Food is industrial and bland, on a good day. There are better luaus to visit.
After all that, is it worth your time and money to visit? Absolutely. You just need to plan ahead.
Now, here's what I'd suggest: Pick two islands. If you want to see the Arizona Memorial and Pearl Harbor, see Diamond Head, witness the surf on the North Shore, and do those South Shore beaches, then Oahu needs to be one location. It can be a perfect first trip vacation that will provide plenty of memories. Fly into Honolulu, stay wherever you plan to stay, do as much as you can on the island, and enjoy every minute.
Then fly to the second island. At that time of year, I'd suggest the Big Island. You can tour Volcano National Park, see something you can't see on any of the other islands (or even on the Mainland) - flowing lava is pretty amazing to see, and the evening glow of Halemaumau Crater from the Jaeger Overlook inside the Park can be the sight of a lifetime. Beaches on the Big Island are more family-friendly, even if more rare than the other islands, but the time spent will be more fun. If surfing isn't in the cards, snorkeling certainly can be. There are many great snorkeling beaches on the Big Island. See as much of the BI as you want, and at the end of your trip, fly home direct from Kona. You'll only have to change islands once, and you'll have two very different experiences.
I don't suggest Maui for two reasons: 1. Yes, there are nice beaches, but they're no better than on Oahu. 2. The Road to Hana is three hours of extremely winding road, on days that could easily be pouring rain. If your grandson isn't driving (and in a rental car, it's doubtful he would be), it can be a really long drive. Then, when you finally get to Hana, you spend a bit of time, and then turn around and repeat that drive all the way back. Once you've done it, it'll be, "Wow, nice, but I'm glad that's over with." Otherwise, Maui can be a non-starter for an active teenager.
Go online and check into the Oahu Revealed and Big Island Revealed books by Andrew Doughty. They are the best bang for the buck travel books you can get. Worth every penny. They also have a phone app you can download that will give you "What's near me right now" kind of information while you're driving around. Very worthwhile.
Questions? Ask away.
Dave