There is an important assumption in this question, namely that Peter, the apostle, wrote the letter of 1 Peter. Not all scholars are agreement with this point. Some say that the Greek of this letter is too sophisticated for a uneducated fisherman. This is all to say that there are some debates when it comes to authorship. With this stated, there is pretty good agreement in terms of from where the letter was written.
Rome is an excellent conjecture. 1 Peter 5:13 mentions Babylon, which is most likely a reference to Rome. The book of Revelation uses the city of Babylon 11 times and most scholars agree that this is a reference to Rome. For some instances, you can read: Revelation 16:19, 17:5, and 18:2. Perhaps, more importantly, no one think that this reference to Babylon is a reference to the actual Persian city!
Moreover, this location of Rome would coincide with Peter’s martyrdom, which is traditionally thought to be in Rome under the persecution of Nero in 64.
In view of these two points, we can be pretty confident that 1 Peter was written from Rome.