There was a considerable population of Jews in Rome as well.
Not as considerable after 49 AD when Emperor Claudius expelled the Jews from Rome.
Peter was not sent to...."just the Jews". His commission included all twelve tribes of Israel [Matthew 10:5-6] and there were millions living beyond the Euphrates: [Josephus "Antiquities" Book XI, Chapter 5, Paragraph 2, lines 5-6].
There were also tribes of Israel living along the shores of the Black sea [ Peter 1:1-2]. These folks were outside of the Roman sphere of influence (as were their Babylonian brethren) and were descended from the other eleven sons of Jacob [Genesis 49]. Indeed, many descendants of these tribes of Israel had been migrating throughout the world since the Assyrian Empire collapsed about 600 B.C.
For Peter to concentrate his efforts in Rome among a small contingent of Jews (House of Judah) would be in direct opposition to His Lord's command to "Go to the Lost Sheep of the House of Israel". These folks had been exiled in 721 B.C. to Assyria [II Kings 17:23] and scripture does not record their return. The House of Judah (Jews) had been exiled to Babylon 125 years later [II Kings 25:11] and Ezra and Nehemiah record many returning to Jerusalem.