This was my third time on the row that I visited Kos. The first was in 2007 for 3 days as island-hopping from Rhodes, the second in 2008 for a week, the third in 2009 for two weeks... and hopefully sometimes for permanent!!
Out of all the Greek islands we have seen,
Kos is our favourite. We are even thinking of retiring and moving there in the future, if everything goes according to the plans...
Mastihari is the place we always stay, for the nice hotel we have found and the beautiful beach. Also as I like windsurfing, this is probably the only place in Kos to practise at your comfort. Although Mastihari is a popular resort on the island, suprisingly you never feel packed.
Taverns by the beach are delicious. Try Vaggos for the best fish and Yannakis for the good red wine. Rent a car for a couple of days and make a tour of the island. You will discover places full on tourists, like Kardamena, and other spots totally untouched, villages hidden up in the mountains and lovely cottages here and there.
Last time in Kos, we took the daily boat from Kos Town to Bodrum, an organized tourist resort in Turkey. Good recommendation to see other places at once!