As an example, we see that members of the churches founded by Paul would make a habit of visiting the Jerusalem church and its leadership.
• For example, we read in Acts 15 how members visited to sort out doctrinal questions which they deferred to the Jerusalem leadership.
• For another example, we know many Jewish Christians from Paul's churches would visit during their multiple visits to the festivals that were centralized in Jerusalem, e.g. Passover. See below.
• Richard Bauckham: “We should also not forget that the Jerusalem church would have played a unique role in the spread of the Christian Gospel in the Diaspora, …also by preaching to the thousands of pilgrims from all parts of the Diaspora who came to Jerusalem every year for the festivals and who could take the Christian message back to their own communities.” [James: New Testament Readings (Routledge, 1999), 18.]
We know that early Jewish Christians habitually pilgrammaged to Jerusalem to attend the important Jewish festivals there.
In the ancient Mediterranean world and Jewish or Greco-Roman society in particullar, instruction from those who knew the information 1st hand was invaluable. For those who wanted to know the truth of matters, hearing witness-testimony first hand was paramount.
We see this fascination with first-hand testimony (out of the horses mouth) in several sources. For consider these few:
This is relevant because for Christians who wanted this kind of personal instruction, visiting the Jerusalem church where the apostles and central witnesses resided and recounted their experiences was the natural destination.