Places to visit on Big Island:
-Drive to Hilo and take the helicopter ride to see the lava flow
-See sea turtles in the wild - talk to locals and they know where they are
-Visit the Hilton Resort: you don't have to be a guest to visit - it's like a mini disneyland. Take their boat ride (all free)
-Visit volcano national park as the other post suggested
-There is a national historical park not too far from the airport. Scenery there is very beautiful.
-Take the Atlantis submarine 100+ feet underwater (the submarine ride is available on Maui and Oahu too)
-Drive around the island
Big Island doesn't have white sandy beaches - it's known for coal black sandy beach from volcano ash. It's more laid back and less commercialized compared to other islands. Have fun!