It is my understanding that the language of Israel at the time was Aramaic and it that it was also widespread beyond Israel. The Jewish historian Josephus (37AD - 100AD) points this out when he explains how people from what are now Iran, Iraq and remote parts of the Arabian Peninsula knew all about the war of the Jews against the Romans due to the books he wrote "in the language of our country", books which he then translated into Greek for the benefit of the Greeks and Romans.
Josephus also wrote "I have also taken a great deal of pains to obtain the learning of the Greeks, and understand the elements of the Greek language, although I have so long accustomed myself to speak our own tongue, that I cannot pronounce Greek with sufficient exactness; for our nation does not encourage those that learn the languages of many nations."
—Antiquities of Jews XX, XI
I think this provides reasonable evidence that Greek was not a common language for the region at that time.