Peter addresses his epistle to the "chosen exiles of the dispersion", he uses the word diasporas (Diaspora, dispersion). So the immediate context would be to Jewish Christians of the Diaspora in the region of Anatolia/modern Turkey ("Pontus, Galatia, Cappadocia, Asia, and Bithynia").
But it seems errant to assume that Peter is excluding Gentile Christians, consider for example 1 Peter 2:10, "Once you were not a people, but now you are God's people; once you had not received mercy, but now you have received mercy." A statement that doesn't exactly make a whole lot of sense if Peter is speaking explicitly to Jewish Christians, since obviously as Jews they were a people, the Covenant people and nation called by God at Mt. Horeb.
Instead it seems Peter takes the language of exile and applies it spiritually to the Church. The Jewish Diaspora is was physically in exile, but the Church exists in a spiritual diaspora, as pilgrims, strangers, here in this world.
The holy nation, the royal priesthood, is the Church; comprised of both Jew and Gentile.
Peter was Apostle to the Circumcision and Paul Apostle to the Gentiles; but that doesn't mean that Peter never addressed or engaged with Gentiles, or that Paul never addressed or engaged with Jews--it is clear enough from the Paul's letters that he includes Jewish believers in his letters because he includes all believers in his letters; and in his ministry as described in the Acts of the Apostles Paul regularly spends his time in synagogues and engaging with fellow Jews. Likewise, the Acts records the first Gentile converts coming to the faith from Peter's preaching.
It would, therefore, be errant to assume that Paul only concerns his letters for Gentile Christians, because that is not the case; and equally errant to assume Peter only concerns his letter(s) for Jewish Christians. There are not two classes of Christains, one Jewish and one Gentile--there is instead the one, united, new people in Jesus Christ, who are all sons and daughters of Abraham by faith. The olive tree contains both natural branches and wild branches which have been grafted. Jew and Gentile, circumcised and uncircumcised, together as one People of Jesus Christ.
-CryptoLutheran