In this small Greek Island you will always find something interesting to do, and some new places to visit.
You will be pleased to experience the untouched nature, towns like an open museum, beautiful beaches, traditional tavernas, local food, the archeological museums, walk through the old houses and meeting local people. 
On the official information page for Kos Island you will find many options for sightseeing. 
Here you can visit the page and surf through the other pages to make plans for your free time.
P.S: The photograph was taken from Wikipedia Commons, By roogi [CC-BY-2.0 (], via Wikimedia Commons