First of all, there is no place in the New Testament where there is any hint or any record of any kind that Peter was in Rome. In 1 Peter 5:13, it tells us very plainly that he wrote that epistle from the city of Babylon [In Peters day Babylon was still a city and a territory—See Josephus, Antiquities, Book xv, Ch 2, 2. “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]. This is far to the east of the Roman Empire and not in Rome which is in the western part of the Empire. This is where Peter apparently had much of his ministry among the many Jews scattered there from previous centuries. He was there preaching that the Messiah had come, that Jesus Christ was that promised Messiah, and that Jesus Christ was the only hope of salvation. He was there preaching to those people when he wrote the epistles of 1 and 2 Peter. He wrote to those who were in what is now Asia Minor or what is now modern Turkey. All of these districts that he mentions are in a little section of eastern Turkey. The New Testament gives no statement or hint whatever that Peter was ever in the City of Rome, the Capital of the Roman Empire in his day.
There is some groundless tradition that says Peter was in Rome. One problem with the tradition is that the tradition is full of errors, mistakes, things that are incorrect. If read parts of Josephus, all of the Apostolic Fathers, in English translation. The references are there but in the very context in which the references are found the whole thing was full of things that are contradictory to the New Testament. Therefore being contrary to the New Testament their evidence is worthless.
For instance in the Apostolic Fathers, in THE DIDACHE, or TEACHING OF THE APOSTLES we find a paragraph in which many people wish to use a statement there about Baptism. That reference to Baptism is found in a very short paragraph which contains things that are contradictory to the New Testament. Therefore we cannot give any weight to one little statement that people want to use to help them in their false idea of what Baptism is about. Now whether they are intentional or not is beside the point. The errors are there. So it is an unreliable piece of writing. There may be some things there that are interesting and some things that are helpful and there may be some things that are true, but it is unreliable [The Apostolic Fathers, translated by J. B. Lightfoot and edited and completed by J. R. Harmer, 1973 (rpt of 1891 edition), Grand Rapids: MI, Baker Book House. p. 126].
Josephus’ writings contain so much that is fanciful and even just plain ridiculous that a person has to try to pick out what is fact and what is fiction. You cannot just say Josephus said such and such and say that is a fact; that is true. No, you have to weigh the things that he says very carefully. Is it true? Are there other things in the history of that time that corroborates what he says. You cannot just take it because Josephus said it and say, “that’s a fact!” Many times he contradicts what the Bible says. When he gives the “History of the Jews”, the history of Israelite people, time and time again, he contradicts what the Old Testament says concerning the history of the Jewish people. So you have to be very careful when you read these writings. Old? Yes, they are. Josephus wrote around the time shortly after Christ lived. He probably died shortly after 100 AD, himself. So he was living in old times.