The only evidence for Peter in Rome is Church Tradition. This is however very
early, with apocryphal gospels and writings from the 2nd century mentioning
it, and the excavations in the 60s found a 2nd century shrine (the central
grave around which others cluster in the Vatican Necropolis). So the belief
has perhaps been present since at least the first 100 or so years of the
Church.
It is mentioned by Tertullian, and possibly Origen as derived from Eusebius,
and by the 3rd and 4th century Gospels well established. Clement also
reports Peter's Martyrdom along with Paul's, which strongly implies Rome,
based on inference.
To be fair, we won't get any better evidence than this, for a poor fisherman
from Galilee, and a member of a persecuted, and at this stage, unimportant,
sect. It would not be reasonable to expect more. To think he wouldn't end up
in Rome is silly though, as all roads lead to Rome and Paul was a citizen, with
a Christian community there already. Tacitus mentions how all 'superstitions'
readily flock to Rome, and we know Christians were persecuted there in
Nero's day. Why on earth couldn't a prominent early Church leader end up
there?
You can take it or leave it, but no alternative scenario is as well attested. It
isn't provable beyond trust in these sources, but this is true for a lot of
Roman history, which is dependant upon such written ones.
