He was the apostle" to the circumcision", scripture indicates he was in Babylon, which at that time was a hub of Jewish intellectuals and had a large Jewish population.
One thing we know for sure is he was not in Rome as he is not addressed in the letter .
There are some who take Peter's reference to "Babylon" in his letter as a reference to Jerusalem itself. Part of the reason is the view that Jerusalem/Judaism had slipped into apostasy, was persecuting the early church, and, by denying the Messiah was committing spiritual harlotry. Thus the words in Revelation:
"And another angel followed, saying, "Babylon is fallen, is fallen, that great city, because she has made all nations drink of the wine of the wrath of her fornication.'" (Rev. 14:8)
Earlier in Revelation we read: "And their dead bodies will lie in the street of the great city which spiritually is called Sodom and Egypt, where also our Lord was crucified." (Rev. 11:8)
Jesus was crucified by Jerusalem. But it apparently had come to be known spiritually by the name of a number pagan cites.
Also, later in Revlation we read by way of comparison:
"And he carried me away in the Spirit to a great and high mountain, and showed me the great city, the holy Jerusalem, descending out of heaven from God," (Rev. 21:10)
Much of Revelation seems to be about the old Jerusalem vs. the new Jerusalem, the harlot vs. the chaste bride.
I'm not sure there is any evidence to place Peter in literal Babylon.
Beg your pardon...but Babylon had essentially ceased to exist even *before* any New Testament references to it were written. Please cite some authoritative sources attesting to your assertion that 1st Century Babylon was a "hub of Jewish intellectuals and had a large Jewish population."