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.
On the other hand Josephus, Antiquities, Book xv, Ch 2, 2 says . "The ancient city of Mesopotamia, an area which was then a center of pure and uncompromising Judiasim" p. 65, 1 Peter by A. M. Stibbs. ACT 2:9 tells us they were in the Pentecost crowd. "After the fall of Jerusalem in AD 70 Babylonia became, and for centuries remained, a seat of Jewish Schools devoted to the study and interpretation of the law" Dictionary of the Bible, p. 72, by J. J. Davis