Immediately he preached the Christ in the synagogues, that He is the Son of God.
Acts 9:20
Saul went first to the Jewish synagogues to preach Christ. Why?
Because he was Jewish and the people and the place were familiar territory.
Because Jesus came first to the Jews. (John 1:11)
Because the Jewish people would seem to be the most receptive to Christ and the gospel because Jesus was the Jewish Messiah and the King of the Jews. (The first believers were nearly all Jewish, though in short order, they were also the first persecutors of Christians.)
Are there any lessons in this for Gentile Christians?:
First, our initial mission field is naturally those we know and love. This doesn’t guarantee that they will receive Christ, but because they care about us, they are likely to be willing to hear us out—at least at first. Sadly, once hearing that we are Christians, our family and friends, sometimes (often?) reject Christ and do not want to hear it any more. That just means we need to live and love in Christlike ways so that we may earn another hearing at another time. And don’t stop praying for them!
Second, there is nothing wrong with targeting our evangelistic efforts at those who appear to be open. Those who are “religious Christians,” though not saved, are a prime mission field. After praying for the right words, share the gospel with those who know “about” Jesus, but may not know Him.
Of course our Christian witness for Christ and the gospel doesn’t end with people we know or those who may be open. As Jesus said in Mark 16:15, we are to "Go into all the world and preach the gospel to every creature.”