When a foreign citizen needs to contact their Embassy, something has most likely gone the wrong way. However, both Embassies and Consulates also offer harmless functions like reporting a child birth or giving you information if you want to get married in Greece.
All foreign Embassies are located in Athens. Some countries also maintain permanent consulates, honorary consulates and temporary consulates. In case of an emergency you should contact the closest one to the place where you are in trouble but ideally you need to contact the Embassy.
Additionally, you’d probably want to buy travel insurance as it will help a lot with the costs. For example, your Embassy will evacuate you from a natural disaster area but you will need to pay for the service.
Detailed information on the Embassies and Consulates in Greece