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I've done my homework:

Since the reformation one of the oldest anti-Catholic "arguments" used by the Protestants in a attempt to discredit the position and authority of the Pope is the clame "Peter was never in Rome". Thanks to the extensive writings of the early church fathers and a exciting archeological discovery made in the last century We can finally put this Ridiculous "argument" to rest. In a work issued in 1959, Father Kirschbaum, a member of the archeological commission excavating under the basilica during the 1940's, has given a summary of the findings. These are in brief that it is reasonably certain that the place where St. Peter was buried has been discovered.

And

The archeological proof of the existence of St. Peters tomb under St. Peters basilica in Rome.

"Nero...publicly announcing himself as the first among God's chief enemies, he was led on to the slaughter of the apostles. It is, therefore, recorded that Paul was beheaded in Rome itself, and that Peter likewise was crucified under Nero. This account of Peter and Paul is substantiated by the fact that their names are preserved in the cemeteries of that place even to the present day. It is confirmed likewise by Caius, a member of the Church, who arose under Zephyrinus, bishop of Rome [about 200 AD.]. He, in a published disputation with Proclus, the leader of the Phrygian heresy, speaks as follows concerning the places where the sacred corpses of the aforesaid apostles are laid: "But I can show the trophies of the apostles. For if you will go to the Vatican or to the Ostian way, you will find the trophies of those who laid the foundations of this church." And that they both suffered martyrdom at the same time is stated by Dionysius, bishop of Corinth, in his epistle to the Romans, in the following words: "You have thus by such an admonition bound together the planting of Peter and of Paul at Rome and Corinth." [Eusebius, [A.D. 303] (Church History 2:25:5-8)]

This "archaeological proof" STILL doesn't state that Peter was starting churches or presiding in Rome. Paul was executed in Rome but even your proof only says Peter "likewise was crucified under Nero". Nero, as emperor over all of the Roman empire (which included many other countries than just Italy) might have issued the edict to execute Peter, but there is no such evidence that he did so IN Rome. And, even IF he had been martyred in Rome, his bones were never recovered. The bones found in the place thought to be in a general area where Peter's body was cast contained multiple bodies of humans as well as animals so no real confirmation exists that THE Apostle Peter's "relics" reside under the altar in the basilica. It was wishful thinking and used in the middles ages to bilk pilgrims from their money to get the chance to peek at Peter's "grave". There is much legend and very little "proof" that Peter was in Rome much less that his actual remains are what is buried there.