Well....besides the scripture being silent on any venture into Rome or it's environs.....The Word is quite specific on just what Peter is to do....and where to go.
[Matthew 10:5-6] These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not: But go rather to the lost sheep of the house of Israel. Rome was Gentile....and don't tell me there was a large population of Israelites living there.
This is the reason you do not find Peter in Rome. He was an Apostle to the circumcised....."Israelites". [Galatians 2:7-9] But contrariwise, when they saw that the gospel of the uncircumcision was committed unto me, as the gospel of the circumcision was unto Peter (For he that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles:) And when James, Cephas, and John who seemed to be pillars, perceived the grace that was given unto me, they gave to me and Barnabas the right hands of fellowship; that we should go unto the heathen, and they unto the circumcision.....according to the Apostle Paul.
Think about it. Why would it have been necessary for the Lord to commission the Apostle Paul as "The Apostle to the Gentiles" if He was just going to have Peter (and the others) take care of it anyway? [Acts 9:15] But the Lord said unto him, Go thy way: for he is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel.....speaking of Paul. Notice that Paul is given authority to evangelize the The Children of Israel (the circumcised) also....as well as the Gentiles. In addition, he was given authority to bear The Lord's name before Kings. Peter had no such authority.....only to evangelize the "Lost Sheep of the House of Israel" and specifically....to stay away from the Gentiles!
[John 21:15-17] So when they had dined, Jesus saith to Simon Peter, Simon, son of Jonas, lovest thou me more than these? He saith unto him, Yea, Lord; thou knowest that I love thee. He saith unto him, Feed my lambs. He saith to him again the second time, Simon, son of Jonas, lovest thou me? He saith unto him, Yea, Lord; thou knowest that I love thee. He saith unto him, Feed my sheep. He saith unto him the third time, Simon, son of Jonas, lovest thou me? Peter was grieved because he said unto him the third time, Lovest thou me? And he said unto him, Lord, thou knowest all things; thou knowest that I love thee. Jesus saith unto him, Feed my sheep.
All subsequent scripture to the meeting with Paul in Jerusalem....."14 years later" [Galatians 2:1] shows Peter to be engaged in a ministry to these Israelites.....not the Gentiles in Rome.
“...and don’t tell me there was a large population of Israelites living there.”
But there was. There were Jews all over the Roman Empire, and a large colony in Rome. As to Peter’s mission, he was the one who converted Cornelius to Christ, guided by a vision. It seems the Lord amended Peter’s instructions.