The medieval city of Rhodes is a UNESCO World Heritage site and formerly the site of the Colossus of Rhodes — one of the Seven Wonders of the Ancient World. Walk into town, bypassing the first Gate and enter the city at the main Marina Gate.
The streets of this old town which dates back to 407 BC. Venture up the cobblestone Street of Knights to the Palace of the Grand Masters which opens at 8:00 am. A €10 combo ticket is valid for the Palace and the Archaeological Museum.
Walk past the Temple of Aphrodite and exit the walled city to catch the first Rhodes Little Red Train (€7), a 45 min tour “around the more out of the way sights of Rhodes town”. The “station” is on Pl. Eleftherias in front of Aktaion bakery (a worthy stop in its own right for inexpensive sandwiches and Greek baked goods). You can walk back towards the walled city for a fascinating 1-mile walk around the outside of the city walls, primarily circumnavigating the Palace of the Grand Master, past strewn stone cannonballs, before reentering the ancient city via a moat entrance near the Gate of St Antonios.
The Archaeological Museum entrance is part of the combo ticket. This is a huge and interesting museum with lots to see. The streets back to the ship are packed and highly festive with shops and cafes lining our route out to the Gate of Virgins, which is closer to the ship.
A really good city map of Rhodes: http://ontheworldmap.com/greece/city/rhodes/rhodes-city-old-town-map.html