Why did Paul go to Rome after being held in Caesarea?
He appealed to Rome after a year and a half in prison at Caesarea, and was therefore sent by ship toward Rome. The move to the imperial capital was the required legal route following that appeal, and the context presents it as the necessary outcome of that appeal.
Les explains that Paul had to appeal to Rome after spending a year and a half in prison in Caesarea, and so he was on a ship headed for Rome. Les also notes the remarkable nature of this little Jew going almost without fear into the capital of the pagan Roman Empire, which was now beginning to turn on Christianity. The Romans generally tolerated ancient Jewish religion, even protecting temple tithes and offerings, but persecuted Christianity because they viewed it as relatively new and because it claimed a king with power above Rome.