The beaches at Kos Town, such as they are, are not very good. Better beaches are found in both directions along the coast from the town at Lambi and Psaladi. The ones on the road to Psaladi, past the new Kos Marina are quite pleasant, close to a fair few tavernas, and offer great value for money too. The one we frequented did two sunbeds, one upright chair, an umbrella, a table and two bottles of mineral water for 5 euro! These beaches are within easy reach if you've hired a bike and they have proper bike parking racks too.
This dolphin fountain, a local landmark is at the centre of what is referred to as "Dolphin Square". Although it's not a square but a traffic roundabout, it is a focal point of the harbour area.
One of the great "must sees" of Kos Town is "Hippocrates Plane Tree". There can be no doubt that Hippocrates did not teach under nor indeed plant this tree, as it is nowhere near old enough for either of these legends to be true. It is about 700 years old and is possibly descended from (if trees can have descendants) and on the site of a tree under which Hippocrates taught.
It's an impressive sight nonetheless - the trunk of the tree has split into three parts with a considerable gap between the three segments, and yet it lives on. It is supported by some quite ungainly looking scaffolding, and the tree almost engulfs the old well of the nearby Loggia Mosque. If you're a German tourist you can ignore the "keep out" signs and go and clamber inside the tree, all in the name of a better photo. :-S
A visit to Kos came as a welcome, unplanned, surprise on our visit to the Dodecanese Islands in May 2005. We were based on Rhodes and took advantage of a day trip here instead on some of the smaller islands which didn't fit in with our schedule.
My impressions were of a greener city than Rhodes and much more of a turkisk feel to it - no surprise really as the Turkisk coastline is only a few miles away and is clearly visible. There was much to see with the many archaelogical ruins and the castle of the Knights of St John right in the centre and the harbour front to enjoy. About 5 hours for our day trip here - long enough for a first visit but I'm sure there is much we didn't see too. It sounds like the rest of the island is well worth exploring too.
A visit to the castle in the centre of town is a must if only for the views from the walls.
Other ancient ruins abound around the town.