When Peter writes his first epistle he addresses it to [I Peter 1:1] To God's elect, strangers in the world, scattered throughout Pontus, Galatia, Cappodocia, Asia, and Bithynia who have been chosen according to the foreknowledge of God the father. These folks were Israelites along the southern shore of the Black Sea in an area that Paul was told to stay out of [Acts 16:7]. The order in which Peter names the provinces of Asia Minor (east to west and back) clearly proves that this letter was sent from Babylon in the east....not Rome in the west.
Peter's manner of speaking and writing was not apocalyptic...it was plain...almost blunt. He would never inject anything mystical about his whereabouts. It was not until after Peter died that Rome was even suggested as a possible modern Babylon by John in chapter 17 of Revelation.
I always come back to [Acts 28:21-22] "And they said unto him, We neither received letters out of Judaea concerning thee, neither any of the brethren that came shewed or spake any harm of thee. But we desire to hear of thee what thou thinkest: for as concerning this sect, we know that every where it is spoken against." These words, of course, being spoken by the leaders of the Jewish community in Rome upon Paul's arrest and arrival there. Doesn't it seem likely that these Jewish leaders would have heard more than this....about this sect.....if the Apostle Peter had been setting up the church at Rome and ostensibly recruiting Jews....because that was his responsibility [Galatians 2:7].
And what a perfect place to mail an epistle to the sojourners in Asia Minor, delivery by caravan express.