The Archaeological Museum of Paros sits just behind the Ekatontapiliani church and is worth the small admission fee for the star exhibit alone: a fragment of the Parian Chronicle, a 3rd-century BC marble inscription that reads like a timeline of Greek history.
The collection also includes pottery, sculpture, and finds from the ancient city of Paros, including a vivid 7th-century BC amphora depicting the Gorgon Medusa. The Cycladic figurines are good, and there are pieces connected to the poet Archilochos, one of the most important lyric poets of ancient Greece, who was born on Paros around 680 BC.
The museum is small enough to cover in under an hour, and the garden is a pleasant place to sit after you have finished.