Both EU and non-EU citizens may purchase property anywhere in Greece with the exception of a few designated areas near the borders. Since 1991 when Greece opened up to foreign buyers there has been a steady influx of foreign investors, some buying up land and houses to relocate to Greece while others are buying holiday homes. The last five years have seen a boom in property prices and some of the islands in particular are becoming inundated with new buildings and real estate offices. Shop around and compare prices. You will need to appoint a lawyer ('dikigoros') in accordance with Greek law to make a property purchase. The lawyer conducts the title search at the relevant land registry.
A civil engineer ('politikos michanikos') may be hired to review a specific plot and to ensure that boundaries are within the description in a title document. They can also be consulted regarding specific building restrictions in place in your chosen area.