29 Grk “the one in Babylon,” which could refer to some individual woman (“she who is in Babylon”) since the Greek article (here “the one”) is feminine. But it is much more likely to be a veiled reference to a church (the Greek word “church” is also feminine in gender).
30 Most scholars understand Babylon here to be a figurative reference to Rome. Although in the OT the city of Babylon in Mesopotamia was the seat of tremendous power (2 Kgs 24–25; Isa 39; Jer 25), by the time of the NT what was left was an insignificant town, and there is no tradition in Christian history that Peter ever visited there. On the other hand, Christian tradition connects Peter with the church in Rome, and many interpreters think other references to Babylon in the NT refer to Rome as well (Rev 14:8; 16:19; 17:5; 18:2, 10, 21). Thus it is likely Peter was referring to Rome here.
31 Grk “chosen together,” implying the connection “with you” in context.

In other versions

She who is at Babylon, who is likewise chosen, sends you greetings, and so does Mark, my son.

She who is in Babylon, chosen together with you, sends you her greetings, and so does my son Mark.

She who is in Babylon, chosen together with you, sends you greetings, as does Mark, my son.

Your sister church here in Babylon sends you greetings, and so does my son Mark.

She who is in Babylon, chosen the same as you, greets you, and so does my son Mark.

The church that is at Babylon, elected together with you, saluteth you; and so doth Marcus my son.

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