Just off Platea Platanou (plane tree square), a stone bridge carries one over the former moat to the entrance of the Castle of the Knights of St John (Tu-Sun, 8:30-3).
This combined with the castle across the strait in Bodrum comprised the outer defenses for the island of Rhodes. After the 1495 earthquake the Grand Master d'Aubusson rebuilt the walls and further fortified them with an outer enceinte.
He unfortunately demolished or borrowed heavily from the Agora and other ancient structures to do so. The masonry is a mixture of various stones with ancient inscriptions and the knights' coats of arms. Within the castle's antiquarium are many ancient pieces from around the island.
Kos has several archeological sites in the Seraglio Quarter some of which were revealed after the earthquake of '93. The Hellenistic Altar of Dionysus, the ruins of the Central Baths and Vourina Spring and the Casa Romana (Tues-Sun, 8:30-3, fee) which has nice mosaics and offers a good idea of the opulence and spaciousness of wealthy homes of the period.
Farther west by the Catholic Church on Grioriou St. is the Roman Odeon (theater). Just opposite are the Western Excavations which reveal a mix of historical periods. There are massive Hellenistic walls built around the Acropolis, now studded with a minaret. There's a gym with 17 restored Doric pillars. Opposite are the marble paved main streets of Roman Kos lined with ruined ancient domiciles, especially the House of Europa. The ancient stadium is a block north.