It's more difficult for those of us not from the EU to be longterm residents in Greece. I have heard renewing the residence permit can be a hassle and it expires while you are out of Greece, they will not let you back in! One might think that before the initial three months is up, you could make a trip to Brindisi or Venice and then make another three-month entry, but they might frown on that...
A website for Americans living in Greece,
A United States citizen may enter and remain in Greece for up to three months without a visa. At the time of entry, a stamp is placed in his/her passport showing the date and point of entry. If the planned visit is to exceed the three months, he/she must request, like any other alien, a residence permit from the Aliens Police at least fifteen days prior to the expiration of the original three month period. A residence permit for an additional three months, a total of sic months from date of entry, can be granted if the individual can prove to the satisfaction of the authorities that he/she is in possession of sufficient means of support to finance his/her stay. The purpose of the requested extension and possible intention fro a prolonged stay in the country are seriously taken into consideration. It should be expected that residence permits for stays beyond the six months may not be easily granted and the Greek authorities will not give advance assurance that the individual will be permitted to prolong his/her say. All applications to the local aliens authorities will be forwarded to the Ministry of Public Order for consideration.
But do not be deterred, Albo2! There are Americans living in Greece who have found a way to make it work. (I am assuming you do not hold dual Greek-American citizenship.)