If Peter was in Rome, as you like to think, well then, consider Rome and all its institutions as spiritual Babylon, nothing is stopping you.
Personally, I believe that he was in Jerusalem, right where the bible places him. Sorry, it comes from Baal, as that place was where the Chaldeans lived and worshipped their god. Ba-bel. The Chaldeans were very confused, worshipping the created thing, the sun and the stars, not the Creator.
I don't know what to tell you, but your etymology is dead wrong.
If Peter was in Rome, as you like to think, well then, consider Rome and all its institutions as spiritual Babylon, nothing is stopping you.
I don't think it does any harm to think of pagan Rome in the 1st Century as "confused," before Paul and Peter and his successors evangelized it. (Where again does "Babylon"="confusion?")
Babylon is a code-word for Rome. It is used that way multiple times in works like the Sibylline Oracles (5:159f), the Apocalypse of Baruch (2:1), and 4 Esdras (3:1). Eusebius Pamphilius, in The Chronicle, composed about A.D. 303, noted that “It is said that Peter’s first epistle, in which he makes mention of Mark, was composed at Rome itself; and that he himself indicates this, referring to the city figuratively as Babylon.”(*) Loraine Boettner, "Roman Catholicism".Consider now the other New Testament citations: “Another angel, a second, followed, saying, ‘Fallen, fallen is Babylon the great, she who made all nations drink the wine of her impure passion’” (Rev. 14:8). “The great city was split into three parts, and the cities of the nations fell, and God remembered great Babylon, to make her drain the cup of the fury of his wrath” (Rev. 16:19). “[A]nd on her forehead was written a name of mystery: ‘Babylon the great, mother of harlots and of earth’s abominations’” (Rev. 17:5). “And he called out with a mighty voice, ‘Fallen, fallen is Babylon the great’” (Rev. 18:2). “[T]hey will stand far off, in fear of her torment, and say, ‘Alas! alas! thou great city, thou mighty city, Babylon! In one hour has thy judgment come’” (Rev. 18:10). “So shall Babylon the great city be thrown down with violence” (Rev. 18:21).
These references can’t be to the one-time capital of the Babylonian empire. That Babylon had been reduced to an inconsequential village by the march of years, military defeat, and political subjugation; it was no longer a “great city.” It played no important part in the recent history of the ancient world. From the New Testament perspective, the only candidates for the “great city” mentioned in Revelation are Rome and Jerusalem.
“But there is no good reason for saying that ‘Babylon’ means ‘Rome,’” insists Boettner [(*)]. But there is, and the good reason is persecution. The authorities knew that Peter was a leader of the Church, and the Church, under Roman law, was considered organized atheism. (The worship of any gods other than the Roman was considered atheism.) Peter would do himself, not to mention those with him, no service by advertising his presence in the capital—after all, mail service from Rome was then even worse than it is today, and letters were routinely read by Roman officials. Peter was a wanted man, as were all Christian leaders. Why encourage a manhunt? We also know that the apostles sometimes referred to cities under symbolic names (cf. Rev. 11:8).
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William A. Jurgens, in his three-volume set The Faith of the Early Fathers, a masterly compendium that cites at length everything from the Didache to John Damascene, includes thirty references to this question, divided, in the index, about evenly between the statements that “Peter came to Rome and died there” and that “Peter established his See at Rome and made the bishop of Rome his successor in the primacy.”
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[Archaeological] evidence had mounted to the point that Pope Paul VI was able to announce officially something that had been discussed in archaeological literature and religious publications for years: that the actual tomb of the first pope had been identified conclusively, that his remains were apparently present, and that in the vicinity of his tomb were inscriptions identifying the place as Peter’s burial site, meaning early Christians knew that the prince of the apostles was there. The story of how all this was determined, with scientific accuracy, is too long to recount here. It is discussed in detail in John Evangelist Walsh’s book, The Bones of St. Peter. It is enough to say that the historical and scientific evidence is such that no one willing to look at the facts objectively can doubt that Peter was in Rome. To deny that fact is to let prejudice override reason.
There are numerous patristic references to Peter leading the Church from Rome, see Peter's Roman Residency