Where It All Goes Down
First-Century Roman Empire
The action in the Gospel of Luke was confined to the Jewish homeland in Judea. Jesus liked to work neighborhoods he knew. But Acts of the Apostles spans far and wide. Even Jesus predicts that the apostles will be his "witnesses in Jerusalem, in all Judea and Samaria, and to the ends of the earth" (1:8). He wasn't kidding.
In The Beginning
Acts begins in Judea around 30-something CE. The opening chapter starts right after Jesus has died and risen again. Forty days later Jesus ascends into Heaven (1:9). Ten days after that the apostles all get visited by tongues of fire (2:1-4). It was a busy month and a half.
So when Peter and the other apostles start preaching in and around Jerusalem, it's at great personal risk. Remember—the religious authorities in the city had just turned Jesus over to the Romans to be crucified. Yeah. So the twelve apostles weren't exactly talking about the most popular guy in town when they mentioned Jesus's name.
After Stephen is killed and folks in Judea decide to start openly persecuting Christians again, the disciples start to branch out (11:19). The whole stoning thing made them realize that they might not want to put all their eggs in one basket. Enter Paul (post-conversion) and his band of traveling disciples.
Across The Empire
Paul touches base with the apostles in Jerusalem before taking a trip to Antioch (which was near his hometown of Tarsus) to work on building the church there (11:25-26). When the Holy Spirit taps him to start spreading the gospel far and wide, Paul is definitely up for taking a trip around the eastern half of the Roman Empire.
Back in the first century, the Romans were large and in charge. Throughout the Empire, conquered people were required to pay homage to Roman gods or to pay the price for crossing Rome. Believe us, that is one price you did not want to pay. The folks in Judea were under Roman control and they didn't much like it either. Even though Jews were granted an exception to the whole worship-Roman-gods-or-die law, they didn't take too kindly to their occupiers. In 66 CE, they actually tried to kick Rome out of Judea. Things did not go well.
A Paul For Every City
Every time he goes to a different place, Paul runs into different problems. In each city he arrives, Paul first seeks out the local Jews and visits the synagogue to preach about Jesus (13:5, 14:1, 17:1, 18:19, 19:8). If the Jews in town aren't receptive, Paul tries the local Gentile population.
But things don't always go too smoothly with the Gentiles either. In Lystra Paul and Barnabas are worshiped as gods. Roman gods (14:11). In Ephesus they tick off some of the local craftsmen who think that the Christians are trying to put them out of the idol-making business (19:27). The truth is they are, but Paul decides it's best not to mention that to the angry mob.
No matter where he goes, Paul keeps his setting in mind. When he's in a synagogue, he appeals to his audience's Jewish sensibilities by quoting Hebrew scripture left and right. Makes sense. But since that wouldn't work with a Gentile audience, Paul uses different tactics with these folks. When he arrives in Athens and sees the city is covered in idols, he doesn't outright denounce their gods. Instead, he appeals to them on their terms:
Athenians, I see how extremely religious you are in every way. For as I went through the city and looked carefully at the objects of your worship, I found among them an altar with the inscription, "To an unknown god." What therefore you worship as unknown, this I proclaim to you. The God who made the world and everything in it, he who is Lord of heaven and earth, does not live in shrines made by human hands. (17:22-24)
That Paul is a real pro.
Peter And Paul's Excellent Journeys
All of this leads us to a pretty good question: Why does Paul change setting so often, but Peter hardly ever does?
You can sort of divide the story by its setting shifts. The first part features Peter and takes place in Judea. The farthest he gets away from home is Caesarea, which is about 75 miles north of Jerusalem. Way to explore, Peter. The second part is all about Paul and his travels around the Empire, which take him all the way to Italy. Sure, there's no place like home, but there must be something more going on here.
It probably had to do with their backgrounds. Peter and the other apostles grew up in the Jewish homeland. They were raised in Jewish homes and associated with other Jews. They were probably just more comfortable appealing to Jews rather than Gentiles. Paul on the other hand, was raised Jewish in a Gentile area in Tarsus. In other words, he lived and worked among Gentiles his whole life.
Paul also would have been familiar with the kinds of things that were taught in Greek universities. While he knew Hebrew and received an excellent Jewish education, it would have been easier for him to mix with and appeal to non-Jews. Even Festus says Paul is suffering from "too much learning" (26:24). Even though it's clear he doesn't mean it in a good way, it's obvious Paul has a top-notch educational background. Meanwhile, Peter and the apostles are described as "uneducated and ordinary men" (4:13). Advantage: Paul.