Gythion

Gythion is not an island. It is a town on the southwestern part of the Peloponessean Penisula. You could visit Monemvasia or Byzantine Mystras, near Sparta, from there. Doesn’t your ship provide options?Or hire a driver?

Gythion (aka Gythio or Gytheio) is not an island -- it's a seaside town in the Peloponnese region of Greece. Just Google Gythion Greece and you'll find lots of information. There's one Trip Advisor post about what to do on a cruise stop there, and also some You Tube videos. I've not been there but it looks like a great place.

Gythio was the port for Sparta. It is a pretty town however I would consider renting a car and driving to visit Mystras at present day Sparti. This was the last city of the Byzantines and is an extensive site down the mountainside. It will take about 4 hours to do properly.
Or go west to Monemvassia. It is a 14th century walled town with the remnants of a fortress on top of the mountain. Also known as the Gibraltar of Greece. It is a completely different experience to Mystras.
As I recall both sites can be reached within about 45 minutes from Gythio by car.
Images of both these sites can be seen towards the end of my Nafplion album.
Nafplio and Peloponnese http://www.flickr.com/photos/stanbr54/sets/72157632094108982/

Gythion has a nice waterfront full of restaurants and cafes. We passed through last year and didn't stop, but it seemed pretty. Another alternative is to visit Diros Caves, which are fantastic if indeed they're open in October. The pebble beach nearby has remarkably clear water. We love Byzantine art and architecture, but I have to say Mystras was underwhelming, despite its superb location. (IMHO) Monemvasia is quite far from Gythion. For all three options, you'll need a car.