17 nor did I go up to Jerusalem to the apostles who came before me, but I went into Arabia and later returned to Damascus. -Galatians 1:17 BSB
After Paul received the Holy Spirit and got baptized, he spent many days with some of the disciples in Damascus, see Acts 9:10-19. Most likely, right after his short time with the disciples in Damascus who helped Paul after he got saved, he left for Arabia. It doesn’t say where in Arabia he went to nor the city he visited.
It seems he didn’t spend too much time in Arabia unless Damascus was in Arabia, and he went to a different location in Damascus. Acts 9:20 says that he started preaching in Damascus, maybe where the disciples who helped him lived. Wherever Arabia was at, Acts 9 says that Damascus is where Paul began to preach the gospel of Jesus Christ without first visiting Jesus’ Apostles. After Paul’s conversion, the Holy Spirit gave him spiritual understanding and insights about Jesus being the Son of God and how he could prove it, using the Scriptures, see Acts 9:20-22.