The apostle paul traveled to many places after he became a disciple of Christ. He planted churches in Rome and many other places he visited these churches on his journey to make sure that they kept sound Christian doctrines. For an exhaustive list of places traveled open your bible and start reading it beginning in the book of acts with Paul's conversion and read Paul's letters romans,Ephesians,collossians Galatians. etc
The journey of St. Paul started with him being known as Saul of Tarsus. He highly persecuted the early disciples of Jesus, and on a mission to Damascus for more persecution, he was converted to Christianity after being struck blind. His blindness was restored 3 days later by Ananias. He then started preaching about the Messiah Jesus as the son of God with James the Just and Simon peter. Read more details at en.wikipedia.org/wiki/Paul_the_Apostle.
^ Answered it as well as can be said in text. I'd recommend trying to find a graphic map outlining his four journeys in different colours. These can often be found in study Bibles, particularly the NIV Student Study Bible.