Saint Peter in Rome
Some might argue that whether Peter went to Rome and died there, is not important simply because his being in Rome does not itself prove the existence of the papacy; it would be a false conclusion to say he must have been the first pope since he was in Rome and later popes ruled from Rome. If this was all it was to it.
Yet, we have to consider that this does not say he still could not have been the first pope. Why? Because one of his successors could have been the first holder of that office to settle there. After all, if the papacy exists, it was established by Christ during His lifetime, long before Peter is said to have reached Rome. Logically, there must have been a period of some years in which the papacy had no connection to Rome.
If the Apostle got there only much later, this could bear on who his legitimate successors would be, since the man elected bishop of Rome is automatically the new pope on the notion that Peter was the first bishop of Rome and the pope is merely Peter's successor. Still, again, this says nothing about the status of the papal office. It would not establish that the papacy was instituted by Christ.
So why is Rome so important and when Peter arrived?
Most anti-Catholic advocates take up the matter and even go to considerable trouble to "prove" Peter could not have been in Rome. Why? Because they think they can get mileage out of it by confusing matters, the shell game or "straw man" argument.
"Here's a point on which we can put the lie to Catholic claims, they say. Catholics trace the papacy to Peter, and they say he was Martyred in Rome, but if we can show he never went to Rome, that would undermine at the very least psychologically, if not logically their declaration with certainty that Peter was the first pope. If people conclude the Catholic Church is wrong on this historical point, they'll conclude it's wrong on the larger one, the supposed existence of the papacy. This is the general thrust of such anti-Catholic assertions.
Perhaps the most well-known is the author of bigoted screed against the Church, Loraine Boettner in his work, Roman Catholicism (p. 117): "The remarkable thing, however, about Peter's alleged bishopric in Rome is that the New Testament has not one word to say about it. The word Rome occurs only nine times in the Bible [actually, ten times in the Old Testament and ten times in the New], and never is Peter mentioned in connection with it. There is no allusion to Rome in either of his epistles. Paul's journey to the city is recorded in great detail (Acts 27 and 28). There is in fact no New Testament evidence, nor any histor- ical proof of any kind, that Peter ever was in Rome. All rests on legend."
Well so what? True, the Bible never unequivocally says he was there; but, an important but, it doesn't say he wasn't. Just as the New Testament never says, "Peter then went to Rome," it never says "Peter did not go to Rome." In fact, very little is said about where he, or any of the Apostles other than Paul, did go in the years after the Ascension. Essentially we have to rely on books other than the New Testament for learning about what happened to the Apostles, Peter included, in later years.
Boettner is dead wrong, however, when he proclaims "there is no allusion to Rome in either of [Peter's] epistles." There is, in the greeting at the end of the first epistle: "The Church here in Babylon, united with you by God's election, sends you her greeting, and so does my son, Mark" (1 Pet. 5:13). Babylon is code for Rome and is used this way six times in the last book of the Bible. In fact one of the chronicles  by Eusebius Pamphilius at the time held "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."
It is interesting to note that when they want to the anti-Papists are wont to refer to Rome as Babylon, in the pejorative sense, so one can logically ask, where did this allusion spring from but from knowing the code in the first place. Like it or not, they cannot have it both ways.
Some might counter, well why are not those other Babylonian references in the New Testament literally about Babylon?
Simply put, Babylon had experienced 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. The only truly "great city" in New Testament times was Rome. It would make no sense otherwise.
"But there is no good reason for saying that 'Babylon' means 'Rome,'" insists Boettner. This is because he neglects to consider the persecution of the early Christians and the need for caution when writing or speaking. Peter was known to the authorities as a leader of the Church, and the Church, under Roman law, was an insult to the accepted religion of Roman paganism. Peter would do himself and those under his charge no service by announcing his presence in the capital whether in writing or otherwise. Saint Peter was a wanted man as the expression goes.
Having said of all this, do I think that all those who do not think Peter was in Rome are ill-intended? No, most of them are not scholars and are going by the Bible only. There seem unaware that before the New Testament books were adopted into the Canon of inspired books, there was almost 400 years of Tradition, the very Tradition that assisted the Church in its adoption of the books of the Bible were to be included and those to be discarded. Ideally skeptics ought to consider secondary sources, one which is that of William A. Jurgens, in his three-volume set The Faith of the Early Fathers, a virtual compendium that cites at length everything from the Didache to John Damascene, 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." From these references and those of similar writings makes it write clear and certain that the universal, and very early understanding was that Peter was in Rome and was Martyred there.
Dionysius of Corinth, writing his Letter to Soter, the twelfth pope, about A.D. 170, said, "You have also, by your very admonition, brought together the planting that was made by Peter and Paul at Rome."
Tertullian, in The Demurrer Against the Heretics (A.D. 200), noted "how happy is that Church ... where Peter endured a passion like that of the Lord, where Paul was crowned in a death like John's" [referring to John the Baptist, both he and Paul being beheaded]. Fundamentalist apologists actually that admit Paul died in Rome, so the implication from Tertullian is that Peter also must have been there.
In the same book Tertullian wrote that "this is the way in which the apostolic Churches transmit their lists: like the Church of the Smyrnaeans, which records that Polycarp was placed there by John; like the Church of the Romans, where Clement was ordained by Peter." Clement, known as Clement of Rome was the fourth pontiff. [Note that Tertullian didn't say Peter consecrated Clement as pope, which would have been impossible since a pope doesn't name his own successor; he merely ordained Clement as priest.] Clement wrote his Letter to the Corinthians perhaps before A.D. 70, just a few years after Peter and Paul were killed; in it he made reference to Peter ending his life where Paul ended his. What could be clearer? After all, it is not as if Tertullian was lying in order to set the state for Protestants almost 2000 years later, unknown to him.
Irenaeus, in Against Heresies (A.D. 190), said that Matthew wrote his Gospel "while Peter and Paul were evangelizing in Rome and laying the foundation of the Church." He then says the two departed Rome, perhaps to attend the Council of Jerusalem (A.D. 49). A few lines later he notes that Linus was named as Peter's successor----that is, the second pope----and that next in line were Anacletus (also known as Cletus) and then Clement of Rome.
Clement of Alexandria wrote at the turn of the third century. A fragment of his work Sketches is preserved in Eusebius of Caesarea's Ecclesiastical History, the first history of the Church. Clement wrote, "When Peter preached the Word publicly at Rome, and declared the Gospel by the Spirit, many who were present requested that Mark, who had been for a long time his follower and who remembered his sayings, should write down what had been proclaimed."
Peter of Alexandria was bishop of Alexandria and died around A.D. 311. He wrote a tract called Penance. In it he said, "Peter, the first chosen of the Apostles, having been apprehended often and thrown into prison and treated with ignominy, at last was crucified in Rome." Lactantius, in a treatise called The Death of the Persecutors, written around A.D. 318, noted that "When Nero was already reigning Peter came to Rome, where, in virtue of the performance of certain miracles which he worked by that power of God which had been given to him, he converted many to righteousness and established a firm and steadfast temple to God." Nero's reign was from A.D. 54-68.
In short and emphatically it should suffice to note that no ancient writer claimed Peter ended his life elsewhere than in Rome. True, many refer to the fact that he was at one point in Antioch, but most go on to say he went on from there to the capital. Remember, these are the works which form the basis of Christian historical writing in the immediate post-New Testament centuries. On the question of Peter's whereabouts they are in agreement, and their cumulative testimony should carry considerable weight.
Thus, it is Boettner who does not know what he is talking about when he claims there is no "historical proof of any kind" and that "all rests on legend." The truth is that all the historical evidence is on the side of the Catholic position.
Continuing, Boettner, like other such apologists, claims that "exhaustive research by archaeologists has been made down through the centuries to find some inscription in the Catacombs and other ruins of ancient places in Rome that would indicate Peter at least visited Rome. But the only things found which gave any promise at all were some bones of uncertain origin" (p. 118).
His original book and the revisions to it failed to mention the results of the excavations under the high altar of St. Peter's Basilica that had been underway for decades, then undertaken in earnest after World War II , concluding some years later.
Pope Paul VI officially announced 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.
Surely it is not impertinent or prideful to say that the combination of historical and scientific evidence is such that no one willing to look at the facts with an open mind, honestly inquiry can doubt that Peter was in Rome. To deny that fact is to let prejudice persuade reason and not the other way around.