There are 2 companies “Adriatic Kayak” (www.adriatickayaktours.com) and “Adventure Dalmatia” (www.adventuredalmatia.com/one-day-activities/sea-kayaking-dubrovnik) both departing from a small beach area by the Pile Gate. For 250 kuna they take you on an organized tour for about 2 ½ hours past the town, along the coast and round the island of Lokrum.
It is easy paddling with stops along the way whilst the guide tells you about the city it’s history and culture, all whilst paddling in and out of the sunset.
There is a stop half way in a cave to have a break, a sand which and to have a drink and a swim to cool down. On return there is a very enjoyable glass of cold wine offered.
I have done this excursion with the family and some girlfriends and can’t recommend it enough.
It is suitable for all ages, though be prepared for extra paddling if you have youngsters! Great fun!