Where did Christianity and Judaism originate - Was it Rome?

Judaism certainly began in the Middle East. While there are questions as to whether Judaism began in Israel/Palestine/Judea/Canaan (all the same place), the Sinai Peninsula, or in Mesopotamia, all of these locations are in the Middle East.

As for Christianity, if the Ministry of Jesus is considered to be the origin of Christianity, then, Christianity began in Roman Palestine. However, if the Ecclesia (the organization of the Church) is seen as the beginning of Christianity, there were great meetings of the Ecclesia throughout the Roman Empire, but primarily in Western Anatolia, Greece, and Tunisia. The Establishment of the Roman Catholic Papacy and the Patriarchates of the Eastern Orthodox Church were primarily in cities like Rome, Byzantium/New-Rome/Constantinople/Istanbul (all the same place), Thessaloniki/Salonika, Ephesus, Tunis, Alexandria, and Damascus.