I think the answer to your question has already been given implicitly in your discussion with /u/michaelnoir: it's Rome. The Roman Empire isn't necessarily where both influences, the Greek and the Jewish, met and mixed for the first time (that had already happened in Hellenistic times) but it's from here where they were transmitted lastingly to later European cultures.

Let me first restate what I wrote in my earlier post: it is pretty much impossible to neatly seperate Roman culture from its greek influences and roots. From its very beginnings Roman culture has been thoroughly hellenized. For example the foundation of Roman law, the Law of the Twelve Tables, was thought to be inspired by Greek legislation, the earliest examples of Roman art are heavily influenced by Greek models and the Romans' expulsion of their last king mirrors the end of Tyranny in Athens. This early Hellenization is easily understandable. When Rome emerged as a sovereign state the Greeks had already colonized much of the Mediterranean and heavily influenced the different peoples of ancient Italy, especially the Etruscans, who in turn were very important for ealrly Rome.

This deep connection was reinforced time and time again when the Romans conquered the Greek cities of Southern Italy and later the Greek east, with the Second Sophistic in the 2nd century AD, or maybe even with the Christianization in Late Antiquity, as Christianity was at its roots one of the many religions of the Greek east. Greek teachers taught the youth of Romes' elites, Greek artists worked on Romes' temples and sculptures, Romes' politicians could speak and write Greek fluently. So when Rome in turn conquered other regions it transmitted its own hellenized culture even to people that had never been much influenced by Greek colonization or the conquests of Alexander the Great.

The Roman Empire is also where the Abrahamic tradition in its Christian form was imparted on a large number of people. Jews and Greeks had already come into contact after the conquests of Alexander the Great and soon large Jewish communities existed in major Greek cities like Alexandria in Egypt or Ephesos in Asia Minor. In Roman times Jewish intellectuals like Philo of Alexandria engaged extensively with Greek thought. But Judaism never became the religion of the majority of the Empire. That role was reserved for Christianity. And the rise of Christianity would probably never have been possible without the Roman Empire inside of which it could initially spread and whos' emperors from Constantine onwards heavily sponsored it. In Late Antiquity Christian intellectuals believed it had been Gods' will that Jesus and Augustus, the architect of the Empire, had been contemporaries. So like with Greek culture it was the Roman Empire that spread the Abrahamic tradition to places it hadn't reached otherwise.

So I hope that I made myself clear that everyone who thinks of himself as a descendant from christian Rome would almost inevitably be led back to ancient Greece und Israel. And already from the earliest Middle Ages christian Rome was the model that the different kingdoms of Western Europe strove to emulate. When the architects of Charlemagne were designing his famous Palatine chapel at Aachen they emulated late antique models that in the end were derived from Greek architecture. When the intellectuals at his court studied the writings of ancient Church Fathers they encountered trains of thought that ultimately led back to ancient Israel. And later when Renaissance thinkers were reading the works of Romans like Vergil or Cicero they were inevitably confronted with Greek ideas and mythology. The fact that Western European societies (and later also those in the Americas) thought of themselves as Christian and as descending from ancient Rome made the connection to ancient Greece and Israel inevitable because Rome was so heavily indebted to Greece and Christianity to Judaism.

Edit: If you are interested in how early medieval societies in Western Europe interacted with greco-roman thought or how much they often identified with Old Testament Israel you should check out Peter Brown, The Rise of Western Christendom. Not a fast read but very informative and engagingly written.