From time to time, Paul mentions "Arabia" and his going there..somewhat "criptically" it seems. In Galatians he mentions "going away into Arabia", before returning to Damascus.

Arabia appears to be a somewhat vague term , oftentimes used to include Petra and the desert area up to the Euphrates river, Damascus, even Lebanon as well as the Arabian desert area itseelf.

Paul never reveals  specifically  where he went, just "Arabia", so I won't hazard a guess and yours would be as good as mine.

But, I am not alone in believing his visit and stay in Arabia was where he first received the teachings from the Spirit of Jesus Christ (sometimes variously  referred to as the Spirit of God).

Remember when he was in Damascus, following the miracle on the road, he was made blind and Ananias was given the mission by Jesus the Christ of returning Saul's  eyesight in Damascus and  telling him that "he is to carry my name before the Gentiles and kings and sons of Israel".

That's what Saul did, kept proclaiming that Jesus is the Son of God in the city, before he was rudely dumped off the wall. That was the extent of his message, so I believe, afterwards, that  he was directed to go to "Arabia", where his learning of the Gospel of God began at the "foot" of the Spirit of Jesus Christ.

The Gospel or evangel that Saul/Paul proclaimed  was always referred to as  "the Gospel of God", never "his" gospel.  

He made it clear that he was simply the "messenger" bringing  the word of God to any and all..paulnbob