The one excursion I will always recommend anyone to do is a trip to Nissyros. There are organized trips from Mastihari which is usually the best way to go about doing it. Boats leave from Kardamena for the 1 hour crossing to the harbour town of Mandraki on Nissyros.
As well as seeing a very different and very traditional island, the biggest attraction is the live volcano.
The crater is in the middle of the island and you can actually walk down into it and see the steam coming out of the holes in the ground and enjoy the smell of sulphur at close quarters!
All in all it is a very interesting and enjoyable day out - even if you choose not to go to the volcano.
The village of Mandraki is picture postcard pretty in parts and there are some good tavernas and beautiful churches, including one in a cave dedicated to the Virgin Mary.
Look at the photos and decide for yourselves
Sailing past Giali where pumice stone is quarried
Coming into the harbour
The approach to the church in the cave dedicated to the Virgin Mary which has a museum and various artifacts on the way
The volcano as seen from inside the crater
The mountains surrounding the crater
........ for more photos