I've been to Hawaii over 20 times and nearly always go directly to the Big Island. There is so much to do there, and so many different climates in one small place. We usually stay near Keauhou, south of Kailua-Kona. There is a great snorkeling beach at Kahaluu Beach Park. Hawaii Volcanoes National Park is a must see, and stop along the way at a coffee plant and a macadamia nut factory, then again in Punaluu to see the black sand beach and swim with sea turtles. Take drinks and snacks since there aren't many places to stop. We've walked on fresh lava flows where the crust is still popping as it cools. North of Kailua-Kona is Hapuna Beach - the best beach on the Big Island. South Point is also a great place - with a green sand beach a short walk away. Explore the island - you won't be disappointed!
If you only have 3 days on the big Island Fly into Hilo and leave from Kona. Although the one way car rentals are a little expensive you will want the time. On the hilo side there is the Volcano National Park, The Moana Loa Macadamia Nut Factory (cK hours for factory operation) The Zoo with white Bengal Tigers and the don't miss Volcano Winery. You can taste test all their varieties for free. They ship to some states unfortunately not mine. However they will pack your wine purchase in egg crates and they guarentee you can check it at the airport and it will arrive safely. We have done twice with all bottles arriving safely. Have given many bottles as gifts and friends now request it from us.
On the kona side check out the Waikaloa area. Great golfing and terrific dining. Have fun Aloha