Methana is an excursion you can make with the motorbikes you rent. (NOTE! All companies do not allow you to go so far away. Ask first) You go west from Galatas towards Trizina. There are signs towards Methana. I went to the other side of the island and the petrol lasted all the way. The trip was about 60 km both ways.
Methana is known for its salutary sulphur bath. You can take a bath in the sea or in one of the public baths you find in Methana.