St. Matthew's Gospel, by all accounts, was originally written in Hebrew and done so specifically to leave a written record of Jesus' teachings for the Jews in Jerusalem.
St. Mark's Gospel was probably written in Rome while he was there with St. Peter, who was undoubtedly his primary source. It's hard to say who this gospel was intended for. Maybe the Jews in Rome? Maybe the Romans? Maybe it was simply written to preserve, for anyone, the memories that St. Peter had of his discipleship under Jesus.
St. Luke's Gospel appears to have been written primarily for Gentiles. He addresses it to a person with rather a Gentile name, but scholars argue whether this was a real person or just a figurative name (theophilus) that stood for all Christians - the name means "lover of God." He did his homework, that's for sure. It certainly stands to reason that the only way he could have known all the intimate details of Our Lord's infancy was to have interviewed the Blessed Virgin herself.
St. John's Gospel ... who can say? It's so other-worldly that it's hard to pin down who the audience might have been. However, since St. John seems to have centered his Gospel around a Jewish liturgical calendar, it could be argued it was written for Jews.
Most of the New Testament was directed to the Jews, and most, if not all of it, was written prior to the destruction of Jerusalem in 70 AD.