Umm...there IS biblical proof of Jesus being in Jerusalem.
I didn't deny that there is. Curtis, listen to me, bro. I asked "whether there is any proof Jesus was in Jerusalem, written when he actually was in Jerusalem?" The Gospels were not written when Jesus was in Jerusalem, hence my statement: "the Biblical record itself is a recording of events that occurred long before the autographs were inscribed".
Also, every other writer uses the word "Rome", when talking about Rome. So why did Peter use "Babylon"?
"Babylon" was used for "Rome" because Peter was the head of the Christian Church. If the authorities under Nero's reign were to intercept his epistle, they would be directed to the location of the prime minister of Christ's kingdom. It's a strategic ploy.
Babylon was then in ruins, and there was no tradition for five centuries that Peter had been there, whereas the tradition connecting him with Rome is one of the strongest in the Church. Babylon is used for Rome in the Sibylline Oracles and in Revelation (cf. 14:8; 16:19; 17:5; 18:2,10).
Also, consider these non-Catholic historians:
"Some Protestant controversialists have asserted that Peter was never in Rome...I think the historical probability is that he was...Protestant champions had undertaken the impossible task of proving the negative, that Peter was never in Rome. They might as well have undertaken to prove out of the Bible that St. Bartholomew never preached in Pekin...For myself, I am willing, in absence of any opposing tradition, to accept the current account that Peter suffered martyrdom at Rome. If Rome, which early laid claim to have witnessed that martrydom, were not the scene of it, where then did it take place? Any city would be glad to claim such a connexion with the name of the Apostle, and none but Rome made the claim...If this evidence for Peter's martydom be not be deemed sufficient, there are few things in the history of the early Church which it will be possible to demonstrate"
G. Salmon "Infallibilty of the Church" (Grand Rapids:Baker,1959) pp. 348-9(a critic of the Catholic faith)
"...to deny the Roman stay of Peter is an error which today is clear to every scholar who is not blind. The Martyr death of Peter at Rome was once contested by reason of Protestant prejudice.'
A. Harnack
'It is sufficient to let us include the martyrdom of Peter in Rome in our final historical picture of the early Church, as a matter of fact which is relatively though not absolutely assured. We accept it, however facts of antiquity that are universally accepted as historical. Were we to demand for all facts of ancient history a greater degree of probability, we should have to strike from our history books a large portion of their contents."
Oscar Cullman "Peter, Disciple, Apostle, Martyr" (London:SCM,1962) p. 114
"That Peter and Paul were the most eminent of many Christians who suffered martyrdom in Rome under Nero is certain..."
F.F. Bruce "NT History" (New York

oubleday,1971) p. 410
"It seems certain that Peter spent his closing years in Rome"
JND Kelly "The Oxford Dictionary of Popes" (Oxford:Oxford,1986) p. 6
"The martrydom of both Peter and Paul in Rome...has often been questioned by Protestant critics, some of whom have contended that Peter was never in Rome. But the archeaological researches of the Protestant Historian Hans Lietzmann, supplemented by the library study of the Protestant exegete Oscar Cullman, have made it extremely difficult to deny the tradition of Peter's death in Rome under the emperor Nero. The account of Paul's martydom in Rome, which is supported by much of the same evidence, has not called forth similar skepticism."
Jaroslav Pelikan, "The Riddle of Catholicism", (New York:Abingdon,1959) p. 36
why worry about what happened to Peter ? Why make up stories about him when they just aren't important?
Because Christianity is a religion based on historical fact. God formed his People over the time in the medium of space and matter. The Eternal Son of God became a man in Palestine in a particular year, and he appointed flesh and blood men to whom he entrusted his pastoral authority with Peter as head of the apostles:
He said to him the third time, "Simon, son of John, do you love me?" Peter was grieved because he said to him the third time, "Do you love me?" And he said to him, "Lord, you know everything; you know that I love you." Jesus said to him, "Feed my sheep." (Jn 21:15-17)
Peter's Roman residency shows that he was indeed the overseer of the Roman Church, which further validates the episcopal office in Rome as being that which rests upon the
Kepha, whom Christ appointed (cf. John 1:42; Mt 16:16-19).