But when it pleased God, who separated me from my mother's womb, and called me by his grace, To reveal his Son in me, that I might preach him among the heathen; immediately I conferred not with flesh and blood: Neither went I up to Jerusalem to them which were apostles before me; but I went into Arabia, and returned again unto Damascus. (Galatians 1:15, KJV)
Note that the KJV translation of Galatians 1:15 is correct in saying "in me," rather than "to me." Many Bibles give "to me" because of the "Road to Damascus" conversion found only in Acts of the Apostles, where Paul actually went first to Damascus and preached only to the Jews there (Acts 9:20: "And straightway he preached Christ in the synagogues, that he is the Son of God").
Arabia in the first century was a term for the land of the Nabateans, with its capital at Petrea, near the southern tip of the Dead Sea. Some theologians suppose Paul went there to preach. If so, he was unsuccessful as there is no record of any converts, and Paul never mentions the Nabateans again.
It is instructive that King Aretas of the Nabateans was at this time also king of Damascus, as a gift from Rome. A very likely scenario is that Paul went to Petrea to seek the king's approval for him to preach to Gentiles in Damascus. The king would have been unconcerned if Paul only preached to Jews, since Christianity was still thought of as a sect of Judaism, but could have ordered Paul's execution if he decided to disapprove of the conversion of pagans. This concern was real, as Paul's success was eventually his undoing, when the governor of Damascus attempted to arrest Paul:
In Damascus the governor under Aretas the king kept the city of the Damascenes with a garrison, desirous to apprehend me: And through a window in a basket was I let down by the wall, and escaped his hands. (2 Corinthians 11:33)