I recommend that you buy Hawaii, the big island revealed, the ultimate guidebook by Andrew Doughty. It is available on line at Amazon and others. We have used his book for Kauai and it is a great book for what to see and what not to see. We have found it to be right on. The one I saw on Amazon for the big island is 2005, but should be recent enough to be dependable for restaurants, etc. Roy's is one great restaurant, although a bit pricey. But you will be in paradise. Depending on your sense of adventure, you must go to Volcanoes National park and find out how to cross the lava to get to the beach where the lava is flowing into the sea. Quite spectacular. We did that a number of years ago and it is quite memorable. The park also has good hiking, including crossing one of the big craters.
We love the Big Island. Its is our favorite island to visit in Hawaii.
Some things to do:
1) Snorkel near Captain Kidd's Monument. Several tour companies can take you there.
2) Volcanoes National Park
3) Mauna Kea to see the sunset. You will need to book a tour company for this trip. Its so cold up there, there is often snow on the ground...in Hawaii! Elevation is 14,000 above sea level.
4) Go to Hapuna Beach. Skip the beach at Waikoloa which is no way near as nice as Hapuna Beach.