Civil weddings on Hydra Island (also known as political or registry weddings) are conducted by the Deputy Mayor of Hydra. You can use the Municipality (Dimos) meeting room to hold your marriage service or any of the outside areas owned by the Municipality of Hydra FREE of CHARGE. This includes any of the island's beaches, the Periptero (band stand above Spilia) or the open squares around Hydra. (Not the Miaoulis Memorial Terrace.)
Alternatives to public spaces also include: at a restaurant or hotel (inside or in their courtyard), private terraces or even on a beach or hillside next to a windmill. Some people who can't marry in church prefer the gravitas that a church adds and are spiritual if not practising in which case there are numerous chapels with outside terraces that are available. Municipality spaces are free of charge. Other places are negotiable. Most restaurants, if you book them exclusively, such as Castello in Kamini, don't specifically add a ceremony area charge.
For lots of ideas and insider knowledge about the pro's and con's of various locations, plus full contact details to book your registry wedding AND how to go about getting your paperwork in order, the wording of your ceremony and much more, please see my Online Consultancy Wedding Planner service.