John MacArthur in his study Bible says the sister in Babylon means a church in Rome and references
Rev. 17:18.
The 1599 Geneva Bible reads, "The Church that is at Babylon elected together with you, saluteth you..." and has a note which says, "In that famous city of Assyria, where Peter the Apostle of the circumcision then was."
The Douay (Roman Catholic) Bible that I have has notes compiled by Bishop Challoner (1691-1781) in it. The note for
1 Peter 5:13 says "Babylon, Figuratively, Rome."
The Spirit Filled Life Bible has the following note at
1 Peter 5:13
"Most scholars suggest that Babylon is a symbolic reference to imperial Rome, with which early church tradition associates both Peter and John Mark. It less likely refers to a sister congregation located in Babylon."