Since Luke tells us that Jews from Pisidian Antioch were among those in Lystra who embittered the minds of the gentiles at Lystra, perhaps it was these same Jews from Antioch who did the same at Iconium, convincing the gentile God-fearers in that city to rise up against Barnabas and Paul. Once they believed Paul was dead after the stoning incident, they may have ceased following the team. In any case, the believers at Lystra witnessed a miracle in seeing Paul arise after he was drug out of the city and supposed dead (Acts 14:19-20), because whether or not he had been dead, after Paul was stoned, he should not have been able to leave Lystra for Derbe on the following day.
We don’t know how long this first missionary journey lasted, but later evangelistic efforts of Paul lasted two to three years. If as I presume, that the apostles left Antioch in Syria in early March of 44 CE, they could have celebrated the Passover that year in Pisidian Antioch. They may have preached there for two or three months before being expelled by the city magistrates at the instigation of the rulers of the synagogue (Acts 13:50), so they may have arrived in Iconium in June or July of 44 CE. Luke tells us the team preached there for a long period of time (Acts 14:3), which may have taken them to the Passover of 45 CE before they had to flee for their lives.
There are no time indicators for their preaching in Lystra, but it was long enough for Barnabas and Paul to raise up a small foundation of disciples for the church there. This may have taken several months before word of the success of the Gospel reached the Jews in Pisidian Antioch and Iconium who convinced the locals there to stone Paul. After Paul’s miraculous recovery and the team leaving for Derbe, they may have spent the winter there preaching the Gospel and founding a body of believers in that city. Luke doesn’t mention any incident occurring there except that they preached the Gospel and taught many (Acts 14:21).
If they left Derbe sometime after the Passover of 46 CE (remember this is allowing for less than a year in each city where Barnabas and Paul raised up church), they could have spent the remainder of the year encouraging the brethren in each city where they preached, reminding the believers that they would suffer persecution (Acts 14:21-22). After doing this in each city, they ordained elders or leaders to oversee and care for the brethren before they finally departed, committing all to the care of the Lord (Acts 14:23).
If it is reasonable to assume Barnabas and Paul left Derbe in May of 46 CE, and spent three months each in Lystra and Iconium, they could have wintered in Pisidian Antioch where they spent the least amount of time of all four cities, because the local magistrates there expelled them. The reason they would have been permitted to stay in Pisidian Antioch at this time is because Sergius Paulus by this time would have been at home, and since he probably would have been the highest ranking Roman official there, the apostles would have been welcome, and their lives would no longer be in danger.
In the early spring, about the first week in March, the ships would again be sailing on the Mediterranean Sea due to the return of good weather, allowing Barnabas and Paul to book passage to Antioch in Syria. It seems they may have spoken the word of God to the folks in Perga while they awaited passage on a ship departing for Syria. The word Luke uses has more to do with speaking or conversing than it has with preaching or evangelizing. Paul and Barnabas may have been laying ground work for a future visit there (cp. Acts 15:39). In any case, when the team arrived in Antioch, they rehearsed all that occurred before the church there (Acts 14:26-27) and stayed in Antioch for quite awhile, according to Luke (Acts 14:28).