Or vice verse I suppose, was there a Little Rome in Egypt (before conquest) or South India where they traded often?
It's probable that there was a Jewish quarter in Rome by the late 1st/early 2nd century CE. From Juvenal's Satire III: hic, ubi nocturnae Numa constituebat amicae, nunc sacri fontis nemus et delubra locantur Iudaeis, – Here, where Numa established his night-time girlfriend, the grove and shrine of the sacred fount are rented out to the Jews.
Athens also had a sizeable population of metics – foreign-born residents who, although lacking political rights, enjoyed a degree of economic freedom (Jones 1986), except the ownership of land or investment in silver mining. Based on the apparent intermingling of metic and Athenian-born populations by marriage ties, leading to Pericles' citizenship law (Aristotle, Athenaion Politeia 26.3) and his own marriage to the foreign-born Aspasia (Plutarch, Life of Pericles 37.2), it may well have been that metics were well integrated into the city.