Nowhere does the Bible claim to tell you everything that happened to the apostles and everything they did even during the time it was being written, to say nothing of afterwards. It doesn't tell you St. John went to Ephesus, but he did. It doesn't tell you St. Thomas went to Iraq and then to India, but he did.
But it's not clear that the Bible knows nothing about Peter being in Rome. 1 Peter 5:13 refers to "she" (the church) "in Babylon". Babylon the city was a ruin when 1 Pt was written, and there's no memory or tradition of Peter going to Mesopotamia in any case. If the people there had been evangelized by Peter, they would not hesitate to tell you so. But the apostle who preached in there country was Thomas, not Peter.
So is "Babylon" a code word for "Rome"? Maybe.
This is not something to even budge an inch over. The only reason people are saying Peter *wasn't* in Rome is because they a priori refuse to accept the importance of the Roman See, and they think denying Peter was ever there is the easiest way to accomplish that.
If "Babylon" in 1 Peter means Mesopotamia and not Rome, then how come the two people with Peter there have Roman names? Silvanus σιλουανοῦ and Marcus μᾶρκος. Pure Roman through and through. Some people say, well, they came from the Roman Empire with Peter. Well ok, where did he get them? If he went to Mesopotamia from Antioch, a Syrian city, or Jerusalem, a Jewish city, then where did he get two Roman companions? If these are just Gentile nicknames for Jews (Silvanus is supposed to be the same person as Silas), then why is Peter using their Roman names and not their Hebrew names in this epistle?? Luke, a Gentile, calls Silas "Silas" in Acts....then all of a sudden, when Peter gets to Mesopotamia he switches to using a *Roman* name? How does that make any sense? Of course if Peter is in Rome, it makes perfect sense.
Second of all, we have the evidence of the Gospel of Mark. Mark, as we know from Eusebius, was the companion of Peter, and wrote down his teaching. It has long been known that Mark's Gospel is full of Latinisms: he uses direct transcriptions of Latin words to a greater degree than any other Gospel. So where did those Latinisms come from, if Peter was in Babylon at the time?
Finally, I see some people are still on that old tired argument about unreliable "tradition". "Tradition", in this case, is not some disconnected, mostly oral theories about where Peter went.
"Tradition" in this case means the entire corpus of Christian literature from the Epistle of Clement (AD. 90s) on. It was unanimously asserted by those sources that Peter was in Rome.
*If* the "Babylon" of the epistle is ambiguous (and I don't think it is as much as people say), then you then consult the subsequent writings, of Irenaeus, of Eusebius, of the presbyter Gaius, and of the certain archaeological fact that Constantine leveled an entire hill to orient the altar of St. Peter's basilica on top of a 1st century grave and a mid-2nd century monument that that may well be the "monument" (tropaion) of the Apostles that the presbyter Gaius talks about visiting in Rome.
The entire body of evidence points to Peter in Rome unless you are theologically predisposed to deny the Roman See her prerogatives.
Which is a horrendous line of argumentation, in my opinion, because earlier generations of Protestant scholars had no problem rejecting the authority of the Roman See but yet accepting quite naturally that Peter was in the city. To wit: http://www.earlychristianwritings.com/1peter.html