Modern Greece is very much part of the West. Western civilisation developed from Greece and the links are strong. But I am thinking that there isn't much to talk about in terms of the relationship between the Western allies and Greece. It looks like it is very much a one way street with the country getting involved with wars and disputes that destroyed its infrastructure in order to support others with very little benefits coming back.
The recent financial crisis has given the Greeks the opportunity to re examine this one way relationship and the debate is very rightly going on about whether Russia is first of all a more natural ally ( for cultural reasons ) and whether a new relationship with them will benefit Greece more. I am in two minds about this but if things continue the way they are then the Hellenic world ( includes Cyprus) should look at a new marriage of convenience!