If the sea, the sun, local bars, and restaurants do not provide enough entertainment for you, the island offers numerous cultural and historical sights and natural beauty that should definitely be seen. You can discover them on your own or in organized tours. By walking, cycling, kayaking or by a 4×4. There are numerous mountain trails and wine routes and climbing rocks. You can rent a motorbike or a boat, join local fisherman and catch your lunch or participate in picking grapes or olives.
See a large variety of activities here.
Do not be merely a tourist in Zavala. Become a local, at least for a brief time.