If you really want to discover Ibiza, take a trip to the north and go walking around the beautiful northern coast.
Start with Portinatx where you will find lots of amazing coves with fantastic clear waters like Cala Xarraca and S'Arenal Petit, take a drive round to San Miguel where the views out onto the sea from cliff edges are really breathtaking and then drop down to the beaches around Benirass to watch the sunset. A truly wonderful day out.