The “center” of the Christian movement (the “Church”, not to put too fine a point on it) was arguably Jerusalem, in the earliest days. That’s where the Apostles were on Pentecost, when the Church was “born”. That’s where they stayed, for that matter. In the book of Acts, we learn of the work done by Peter, James and John, especially, and most of that work was in Jerusalem, though Antioch and other towns do get mentioned, too.
It was to Jerusalem that Paul came, with money from Macedonia and Corinth, to support the Saints, who were gathered there, waiting for the Second Coming of Jesus. It was in Jerusalem that the Jews started the first persecution of the Church, stoning Stephen, throwing one James off the Temple to his death, and killing another with a sword. But, the Saints left Jerusalem: first in the mid-to-late forties, and again, finally, in 70 AD.
In 51 AD, the term “Christian” was first used to identify followers of Jesus. Up to then, in Jerusalem, they were called, variously, Nazarenes or Ebionites. “Ebionite” means “the poor”. They were called “Christians” in Antioch. The term caught on.
Antioch was in what is not Syria. It was Peter’s town, after he left Jerusalem. It could not have been called the “center” of the Church, though, as Jerusalem had been. It was only “a” center. Another, equal in every way to Antioch, was Alexandria. Alexandria was (and is) in Egypt. It was Mark’s city, and for four hundred years, it competed with Antioch to be the “center” of the Church.
North and west of Antioch lay Ephesus, traditionally the city of John, and to the north and east lay Edessa, once capital of the Armenian nation, and seat of the first whole country to adopt Christianity. Well to the west one might have found thriving Christian communities in Corinth, Greece, Thessalonica, Macedonia, and several cities in North Africa, before one came to the capital, Rome. All these cities had thriving Churches, schools and other Christian institutions before Rome. So, for that matter, did Britain, Spain and France. But Rome was the titular capital of the Empire, and so, when Constantine the Great integrated the administration of the Church into the administration of the Empire, Rome, Antioch and Alexandria were chosen as co-equal Patriarchates. Half a Century later, Constantinople (the new capital) and Jerusalem (the old “center” were raised to the same status. By that time, though, Rome had been deserted by the Emperor’s Court and almost all of the government, and in 476 the last western “emperor” was deposed by a German chief and Rome ceased to have any real role in the governance of the Empire that continued to wear its name. The Patriarch was left up to his own devices to keep his branch of the Church alive.