Big Island (Hawaii) has the most diverse climate. Dry as a bone, wet rainforest, mountains, etc. And, duh, can't forget the volcanos!
I think the most popular bike 'tours' are sunrise rides down Haleakala on Maui. It would be a blast (watching sunrise @ 10,000 ft then coasting to the beach), but not exactly extreme exercise.
I would not bike on Oahu, its the most densely populated, is fairly small & the road that circles the island is high-traffic with limited to non-existent shoulders. Add tourists on unfamiliar roads with blind corners & you've a recipe for disaster.