Love the Big Island - We have been there twice.
The last time was 2 years ago and we did a cycling trip around the Island.

Couple of my favorite parts of the ride where riding the IM course from Hana down to the finish and riding from the Black Sand Beach at the southern end up to Volcanoe's National Park.

In the first trip we did a lot of hiking. Volcanoes NP is great to explore and the Big Island Revealed mentions a ranger guided hike thru a lava tube which is much better than Thurston (which has been cleaned up for the tourists) this one is more natural but is restricted to the guided hikes.

Some of the best snorkling I have done is the bay by Captain Cook, where the statue is. It was like swimming in an aquarium with all the different fish.

Have fun.