Saul’s conversion in the first part of this chapter is dramatic, but it will be many years before Saul’s missionary efforts are detailed by Luke. From 9:32 through chapter 12 Luke follows the story of Peter outside of Jerusalem among Hellenistic Jews as well as his arrest in Jerusalem. There is little here to help with chronology. These stories “fit” any time after Saul’s conversion, there is little more to be said about when they occur.
Luke continues to tell the story of the apostolic community moving out from Jerusalem geographically and culturally. While Lydda and Joppa are not too far from Jerusalem and certainly had Jewish populations, they would be Hellenistic Jews in comparison to Jerusalem. Caesarea was a thoroughly Roman city built by Herod as a tribute to the Roman Empire. We have not arrived at Gentile ministry yet, but we are certainly on the edges of what it means to be Jewish. Peter’s ministry here cannot be seen as directed to the Gentiles yet, although in chapter 10 he will be called to preach the gospel to a man who is in fact a Gentile.
This is a good example of Luke’s literary style as well. In these two stories we have a man and a woman healed. This “paired” set of examples is common in Luke’s gospel (Simeon and Anna in the temple in Luke 2, the “lost” parables in Luke 15, etc.) Later in Acts, Paul will preach the gospel to Lydia and the Jailer in Philippi. Luke is also showing that Peter does the same sorts of miracles which Jesus did, although he does them in the name of Jesus. Paul will do similar miracles later in the book (a healing and a resurrection / resuscitation.)
While these two episodes are miracle stories, they give a bit of insight into the way in which the apostolic office functioned in Acts. Peter is traveling in regions which may have been evangelized by Philip. It is possible this is simply to encourage the believers there, doing general pastoral teaching and preaching. But it is also possible that Peter is “inspecting” these believers to see that they have not strayed from the gospel as it was preached in Jerusalem. (Hengel, Between Jesus and Paul, 117; Schnabel disagrees, Early Christian Mission, 1:693; Witherington is open to the idea, Acts, 328).
That these locations are more Hellenistic than Jerusalem may be a hint that Peter is concerned that these “fringes of Judaism” have fully understood who Jesus was. In many ways, Peter is continuing to do ministry like Jesus did, reaching out to people who are Jewish, but on the fringes of society.