Acts 13:6, 13
Perhaps because Barnabas was a native of the island, he and Paul made for Cyprus as the first stage of their so-called first missionary journey. After beginning at Salamis "they travelled through the whole island until they came to Paphos." (Acts 13:6 NIV)
At Paphos Paul and Barnabas met Sergius Paulus, the Roman proconsul, and Paul contended with the sorcerer Elymas who was struck blind by the Holy Spirit.
It is a matter of some debate whether Paul and Barnabas had planned an itinerary beyond Cyprus? Sergius Paulus was a native of Pisidian Antioch and some contend that it was his influence, and power of introduction, that led them to continue in that direction. If so, perhaps this turn of events came as a surprise to John Mark and contributed to his return home? Mark Wilson discusses some of these issues in a paper entitled Saint Paul in Pamphylia: Intention, Arrival, Departure, available here.
I was able to visit Paphos as part of a solo journey around first missionary journey sites in 2012. The site coves a wide area but there are few significant structures to be seen.
Click here for a Google Earth view of Paphos.