According to the United Nations Statistic Division ten countries are classified as Eastern Europe: Belarus, Bulgaria, Czech Republic, Hungary, Moldova, Poland, Romania, Russia, Slovakia and Ukraine.
According to the CIA Eastern Europe is comprised by Belarus, Estonia, Latvia, Lithuania, Moldova and Ukraine
Politically Eastern Europe is associated with the Warsaw Pact (Albania, Bulgaria, Rumania, Czechoslovakia, East Germany, Hungary, Poland, USSR) while Greece was a NATO member [http://upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Iron_Curtain_Final.svg/574px-Iron_Curtain_Final.svg.png]
On the other hand, according to the United Nations Southern Europe consists of Albania, Andorra, Bosnia & Herzegovina, Croatia, Gibraltar, Greece, Italy, Fyrom, Malta, Montenegro, Portugal, San Marino, Serbia, Slovenia, Spain and Vatican City [http://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Europe_subregion_map_UN_geoschme.svg/680px-Europe_subregion_map_UN_geoschme.svg.png]
You can also divide Southern Europe to pure Southern Europe and Southeastern Europe with the latter consisting of Albania, all Former Yugoslavia states, Greece, Turkey and Cyprus.
In any case noone suggests that Greece is a part of Eastern Europe.
ps: Despite the Civil War conflicts in Greece between Royalists and Communists, never was a communist government established.