Here are some historical references that Peter was in Rome and died there.
St. Irenaeus, Bishop of Lyons, Against Heresies 3:3:1, 3:3:2, and 3:3:3, AD 189, "Matthew also issued among the Hebrews a written Gospel in their own language, while Peter and Paul were evangelizing in Rome and laying the foundation of the Church.
"But since it would be too long to enumerate in such a volume as this the succession of all the churches, we shall confound all those who, in whatever manner, whether through self-satisfaction or vainglory, or through blindness and wicked opinion, assemble other than where it is proper, by pointing out here the successions of the bishops of the greatest and most ancient church known to all, founded and organized at Rome by the two most glorious apostles, Peter and Paul, that church which has the tradition and the faith which comes down to us after having been announced to men by the apostles. With that church, because of its superior origin, all the churches must agree, that is, all the faithful in the whole world, and it is in her that the faithful everywhere have maintained the apostolic tradition.
“The blessed apostles [Peter and Paul], having founded and built up the church [of Rome], they handed over the office of the episcopate to Linus. Paul makes mention of this Linus in the letter to Timothy. To him succeeded Anacletus, and after him, in the third place from the apostles, Clement was chosen for the episcopate. He had seen the blessed apostles and was acquainted with them. It might be said that he still heard the echoes of the preaching of the apostles and had their traditions before his eyes. And not only he, for there were many still remaining who had been instructed by the apostles. In the time of Clement, no small dissension having arisen among the brethren in Corinth, the Church in Rome sent a very strong letter to the Corinthians, exhorting them to peace and renewing their faith . . . To this Clement, Evaristus succeeded . . . and now, in the twelfth place after the apostles, the lot of the episcopate [of Rome] has fallen to Eleutherus. In this order, and by the teaching of the apostles handed down in the Church, the preaching of the truth has come down to us.”
St. Dionysius, Bishop of Corinth, Letter to Pope Soter, AD 170, quoted by Bishop Eusebius in Church History 2:25:8, “You have also, by your very admonition, brought together the planting that was made by Peter and Paul at Rome and at Corinth; for both of them alike planted in our Corinth and taught us; and both alike, teaching similarly in Italy, suffered martyrdom at the same time.”
St. Ignatius, Bishop of Antioch, while being brought to Rome for martyrdom, wrote Letter to the Romans 4:3, AD 110, “I issue you no commands, like Peter and Paul: they were Apostles, while I am but a captive.”
Pope Clement (fourth Bishop of Rome), First Epistle to the Corinthians, Chapter 5, AD 96, “But not to dwell upon ancient examples, let us come to the most recent spiritual heroes. Let us take the noble examples furnished in our own generation. Through envy and jealousy, the greatest and most righteous pillars [of the Church] have been persecuted and put to death. Let us set before our eyes the illustrious apostles. Peter, through unrighteous envy, endured not one or two, but numerous labours, and when he had finally suffered martyrdom, departed to the place of glory due to him. Owing to envy, Paul also obtained the reward of patient endurance, after being seven times thrown into captivity, compelled to flee, and stoned. After preaching both in the east and west, he gained the illustrious reputation due to his faith, having taught righteousness to the whole world, and come to the extreme limit of the west, and suffered martyrdom under the prefects. Thus was he removed from the world, and went into the holy place, having proved himself a striking example of patience.”
St. Clement was ordained by Peter, and was mentored by him.