There are lots of activities that you could take part into. Apart from going around the island on a rental car, bike, or ATV, various well organized trips around the island can take you to all the places of interest, from traditional settlements, to archaeological sites, or even the best places to watch a panoramic sunset. Hiking is another option, where you could walk along the well preserved trail on the top of the cliff all along the caldera. Scuba diving is definitely an alternative.The clarity of the water around the island is really incredible! Also visiting another nearby island is possible. A number of businesses renting smaller or bigger yachts exist on the island giving also the possibility of private small trips around the island or nearby islands.
A few ideas on leisure time activities: