To some degree, Judean, Roman, and Carthaginian societies adopted elements of Greek culture. This mostly happened through the natural diffusion that takes place when people of different cultures interact. Of the three cultures, Greek influence on Judea was not as prevalent. The relationship between Judea and the Hellenistic monarchs was unique in that the monarchs had sovereignty over the region of Palestine after Alexander the Great defeated the Persians. Jews did not readily adopt Greek traditions. A major reason for this is the monotheistic religion practiced in Judea was a stark contrast to the many gods worshiped by the Greek religion. Orthodox Jewish groups fiercely opposed Greek influences on their culture and religion. The Jews would respect the authority of the king as long as the king respected the religious and cultural traditions that they held so dearly. When monarchs tried to be too aggressive in acculturating their subjects, especially in terms of religious tradition, the Jews rebelled openly. One Jewish group successfully reclaimed the Holy Land for this reason (the Maccabees.)
That is not to say that the Jews completely rejected Greek influences. Groups known as Hellenists energetically embraced Greek ideas and culture and drew the ire of the authors of some of the Jewish scriptures. The Sadducees were the most recognized of the Hellenists. Archaeological evidence also suggests that synagogues were fashioned after Greek temples and were even decorated with symbols of Greek gods. This points to the fact that, at least aesthetically, images of the Greeks were pleasing to Jews. Of the groups that were dominated by Alexander the Great, the land of Judea assimilated the least.
The Carthaginians were quite receptive of Greek culture and influence. The Carthaginians were originally the Phoenicians from Lebanon. By the time they were fighting against the Romans for Mediterranean dominance in the Punic Wars, they were speaking a language that had a great deal of Greek influence. Carthage adopted Greek systems of warfare and hired Spartan and Hellenistic mercenaries to fight in its military. Similarities also existed in the coin systems and pantheon of gods of Carthage and Greece. Carthage, like the Greeks, established colonies throughout the Mediterranean Sea, which made them a wealthy kingdom. Carthage seems to have eagerly adopted Greek culture.
The history of Greek and Roman interaction actually predates Rome itself, so it would stand to reason that the Greek influence was salient. The Greek city-states had established colonies on the Mediterranean coast of Italy when Rome was just a small farming village. Rome never saw Greece as a threat culturally or militarily. When Rome conquered the entirety of the Italian peninsula, it absorbed Greek people and Greek ideas. Romans adopted Greek ideas of law, justice, architecture, and government. Even during the period of Hellenistic influence, the Romans saw themselves as the protectors of the Greek cities. This would change after Hellenistic kings allied themselves with Carthage during the Punic Wars, but this did not change the fact that Romans were very comfortable in adopting Greek culture. Romans, especially the upper class Patricians, felt that they would be viewed in higher esteem if they acted Greek.