You ever consider that Rome had the LARGEST Diaspora in the world during the first century? That Rome was the CAPITAL of the known world? Why WOULDN'T Peter go there? And that is exactly what history says that he did. "Babylon" is a synonym of corruption and God-lessness of the OT Babylon. Peter and the Christian community are in the middle of this "Babylon".
Regards
The Jews were ordered out of Rome
Act 18:1 After these things Paul departed from Athens, and came to Corinth;
Act 18:2 And found a certain Jew named Aquila, born in Pontus, lately come from Italy, with his wife Priscilla; (because that Claudius had commanded all Jews to depart from Rome:) and came unto them.
So the inspired word of God says that the Jewish community had been scattered.
Jo, you would be amazed what you can find in the scriptures :)