It's true that there are countless hikes around Greece, thanks to its diverse and rugged terrain, but one of the best islands for doing so is in Naxos. The most epic hike? The 3,284-foot ascent to the top of Mount Zeus, starting out from the trail in the town of Filoti. It's the highest peak in the Cyclades, and getting there is bit of a challenge.
If you're feeling real adventurous, seek out the Cave of Zeus. You'll get the distinct feeling that Greek mythology is actually rooted in reality.