What is absent from II Peter is glaring:
* No mention of anyone being with him at all.
* No mention of Jail, Jailors, visitors, hardships from imprisonment, etc.
* No mention of what form his death may be taking, though he states it to be near.
* No mention of where he is or any travels he may have taken lately.
* No mention of where he may be going if anywhere
You're assuming that Peter wrote this letter. There was a resistance in the early church about accepting this epistle in the canon because it was not a given that Peter wrote it. There are a number of scholars who call this work a pseudonymous work because it gives the appearance of being more remote in time from 1 Peter. The principal reasons are because the author refers to the apostles and our ancestors as belonging to a previous generation now dead (3:2-4) and there is a collection of Paul's letters that exist and appear to be well known, but disputes have arisen on how to interpret them (3:14-16). There is also widespread agreement that II Peter depends on Jude and not vice versa. And finally, this epistle refers to "scoffers" who have concluded from the delay of the parousia that the Lord is not going to return. This could hardly be the case during the lifetime of Simon Peter.
So before you go hanging your hat on disproving Peter was never in Rome based on what is absent from II Peter, you may want to do a little more studying. I can't prove that Peter wrote this letter can you?
Peter himself says he's in Babylon. Now unless you can prove him a liar outright, or otherwise show beyond doubt that he's talking in code which he has no reason to do, He's in Babylon.
This is what your position really boils down to because all you have for documentation 1 Pet. 5:13. And yes, Peter would have a darn good reason to speak in code since the Christians were being persecuted in Rome. And we also know that Babylon is a code-word for Rome. It is used that way six times in the book of Revelation and in extra-biblical works like the Sibylline Oracles (5:159f), the Apocalypse of Baruch (2:1), and 4 Esdras (3:1). This link has been posted before but here it is again.
Again, where's your proof. Where are the FACTS.
Since you don't accept our documentation and I can't get anything from you other that 1 Peter 5:13 it looks like we have reached a stalemate. Unless you want to provide proof that Peter actually did write II Peter. That could prove to be interesting.