Paul and his friends reached Tyre after a straightforward journey. I assume that is the point of Luke mentioning the details of this part of the journey to Jerusalem. No doubt, they had been praying for a good journey. Nevertheless Luke tells us more about what they did in Tyre than how they reached there. So what does he mention?
First, he says that they sought out the disciples who lived there. The fact that they had to seek them out indicates that Paul did not know how to contact them. Yet they could not have been hard to find. Whether they were or not, the search highlights the priority of Paul and his friends, which was to meet with other disciples wherever they went.
The stay there of seven days may have been connected to the timetable of the ship. Yet it indicates that Paul and his companions had the opportunity to spend one Lord’s Day in Tyre, which they no doubt used as in other places. Moreover, the stay of seven days points to the hospitality that was shown to them by the believers living in Tyre.
Luke mentions that the disciples in Tyre were in touch with the Holy Spirit, who revealed to them that Paul faced trouble in Jerusalem. They deduced from this knowledge that Paul should not go there. Paul did not share that deduction. Inevitably this means that he was right or wrong in refusing to listen to them. This is not the only time on this journey in which others urged Paul not to go to Jerusalem, so if his decision was wrong, we would have to deduce that he was pig-headed and unwilling to listen to reason. I suspect that as an apostle he was able to interpret the Spirit’s information more accurately than the disciples in Tyre, and he regarded the details as indicating he should prepare for trouble.
At the end of the week, the disciples in Tyre went with Paul and his friends to the boat. Luke must have been struck by the presence of families who came to say farewell. He also mentions that they knelt to pray, which means that any passers-by could see what they were doing. While they would not necessarily deduce that they were Christians, the posture of prayer does tell us that they were not ashamed to pray together in a public place.