Big Island sites
I was born and raised in Hawaii and spent my high school years in Waimea on the the Big Island so here is my two cents.
The following are some things not mentioned on the thread which are great things to do.
The best snorkling on the island IMHO is at Two Step right next to the City Of Refuge. You walk out onto the lava (not sharp but wear flip flops) and go down two steps off the lava into the water. There are turtles, big schools of colorful fish and great variety. Bring your camera if it works under water.
Definitely go to the top of Mauna Kea (14,000 ft), the clearest place on earth to see the largest observatories in the world and the sunset which is a spectacular view way above the clouds. After the sun goes down, go to the visitors center at 9000 ft. There are three 16 inch telescopes available to the public for general viewing and you won't believe what you can see. Other universes, nebulas etc. Definitely worth the trip.
Go to Waipio Valley on the Hamakua Coast. To get there, drive from Waimea through Parker Ranch to Honokaa and turn left at the intersection in Honokaa to Waipio. There is a spectacular view from the top looking down into the valley and if you like, you can take a four wheel drive for hire to the bottom. A regular car can't make it as it is very steep. People still live down there without electricity and grow Taro. There is a great black sand beach, good surfing and waterfalls to observe. You could hike down but you better be in good shape to do it. When we were kids, we hiked down into the valley and up the other side. The scenery is spectacular and King Kamehameha grew up down there.
If you like waterfalls, go to Akaka Falls (442 ft high) further down the Hamakua coast towards Hilo. There is a small parking fee to enter the park but it is worth it.
Hapuna Beach and the beach at the Mauna Kea Beach Hotel are two of the nicest beaches in Hawaii. At the Mauna Kea Beach Hotel, there are 30 or 35 parking spaces set aside for visitors not staying at the hotel. Get there early for a space especially on weekends. It is definitely worthwhile and if you can't get in, go to Hapuna which is next door. I spent every weekend there as a kid in high school.
Last tip. Go to Merriman's in Waimea for the best dinner you will have on the Big Island. They grow their own produce and everything, fish etc is fresh that day. Google Merriman's for their web site.
You will have a great time!