For Peter being in Rome?
If a tomb holding the bones of an elderly male whose feet had been cut off, with an ancient Greek inscription on it that says "Peter is within" (along with a lot of other evidence of ancient Christian veneration of the site), as well as the testimony of every church father who had anything to say on the topic ... if that isn't "credible evidence," what is?
Ignatius (AD 107) refers to Peter and Paul in connection with the Roman church (he ought to know; he knew both Peter and Paul personally).
Irenaeus, 70 years later, speaks of the Roman see being founded by Peter. Cyprian, 70 years after that, refers to the Roman popes as successors of Peter. All of that is still 60 years before Constantine came on the scene, and the building of a basilica over the burial site that stood until its replacement by the current building in the 16th Century.
To simply discount all of that testimony from men who lived so close to the actual events is like saying that we don't really know where George Washington is buried. Oh, sure, there's a lot of people who say he's buried at Mt. Vernon in Virginia, and there's a tombstone there with his name on it, but really -- all that stuff is just a myth, probably invented by Andrew Jackson for political reasons.
I cant take that as serious evidence. That has as much weight as a tombstone with "Vlad is within" in Leningrad.
Ignatius (AD 107) refers to Peter and Paul in connection with the Roman church ... etc etc et al
A good examination of the issues is here ...
http://www.giveshare.org/churchhistory/peterinrome/
To simply discount all of that testimony from men who lived so close to the actual events ...
Paul and Luke lived the closest to those events, yet they don't mention any of this. Neither does Clement, who is earlier than Ignatius, and who wrote an epistle to the Romans. For each quote from some father you give there is another one who lists Linus as the first bishop of Rome.
If there is anything to be learned from the church fathers, it is that they did not have uniform theological beliefs on any topic whatsoever, with the exception of perhaps the deity of Christ.