As to the place from which he wrote, all do not agree. There is, however, no reason that I see why we should doubt that he was then at Babylon, as he expressly declares. But as the persuasion had prevailed, that he had moved from Antioch to Rome, and that he died at Rome, the ancients, led by this sole argument, imagined that Rome is here allegorically called Babylon. But as without any probable conjecture they rashly believed what they have said of the Roman episcopate of Peter, so also this allegorical figment ought to be regarded as nothing. It is indeed much more probable that Peter, according to the character of his apostleship, traveled over those parts in which most of the Jews resided; and we know that a great number of them were in Babylon and in the surrounding countries.
The design of Peter in this Epistle is to exhort the faithful to a denial of the world and a contempt of it, so that being freed from carnal affections and all earthly hindrances, they might with their whole soul aspire after the celestial kingdom of Christ, that being elevated by hope, supported by patience, and fortified by courage and perseverance, they might overcome all kinds of temptations, and pursue this course and practice throughout life.
Thomas R. Schreiner, New American Commentary: Vol.37 1, 2 Peter, Jude. Broadman & Holman, 2003.
1 Peter, SBJT 21.3 (Fall 2017).
Sean Christensen, Reborn Participants in Christ: Recovering the Import of Union with Christ in 1 Peter, JETS 61/2 (2018), 339-54.
Sean Christensen, Solidarity in Suffering and Glory: The Unifying Role of Psalm 34 in 1 Peter 3:10-12, JETS 58/2 (2015), 335-52.
Costi Hinn, 1 Peter with Costi Hinn.
John Piper, Look at the Book: 1 Peter.