According to the Acts of the Apostles, St. Paul crossed to Europe on his second missionary journey, landed at Neapolis (today's Kavala), and preached at Philippi, Thessalonica (Thessaloniki), Beroea (Veria), Athens and Corinth, sailing home from Corinth's port of Cenchreae. All can be visited. Philippi is a UNESCO World Heritage site, and UNESCO dates his visit to 49-50. At Athens pilgrims climb the Areopagus, where he spoke of the "unknown God." Ancient Corinth, where he lived a year and a half, preserves the forum and the bema thought to be the tribunal of the proconsul Gallio. Acts 20 records a later return through Macedonia and Greece.
These are open-air excavations and Orthodox or civic monuments, not Catholic shrines, so the prayer has to be brought to them. Scripture gives the city and the event; the particular spots are identifications of varying strength. Lydia's baptistery by the stream near Philippi and the reservoir shown as Paul's prison are traditional. The monuments at Kavala and Veria are modern memorials: Beroea, or Berea, is today's Veria, west of Thessaloniki, where almost nothing of the ancient city survives and a mosaic monument keeps steps that local tradition identifies as the place of Paul's preaching. The bema at Corinth is, in the excavators' words, "thought to have corresponded" to the tribunal of Acts 18. Paul wrote to three of these communities: the Philippians, the Thessalonians and the Corinthians.
Many programmes add Meteora, Delphi or the islands. None is a Pauline site: Meteora is a group of Greek Orthodox monasteries founded many centuries after Paul, and Delphi matters to his story only because the inscription that dates Gallio was found there. Summer heat at the sites is considerable.
Related questions, answered
Where did St. Paul first preach in Europe?
At Philippi in Macedonia, after landing at Neapolis, today's Kavala, a port on the north Aegean coast. Acts 16 says he sailed there from Troas by way of Samothrace, spoke to women gathered at a place of prayer by the river, and that Lydia, a dealer in purple cloth from Thyatira, was baptized with her household. A modern mosaic monument beside the Orthodox church of St. Nicholas in Kavala commemorates the landing; the exact place is not known.
Source: Acts of the Apostles 16 (NABRE, USCCB): Troas, Neapolis, Philippi and LydiaVisit Kavala (Dimofelia, Municipality of Kavala): the Baptistery of St. Lydia and the Apostle Paul in Kavala
Did St. Paul visit the Greek islands?
Acts mentions ships passing or calling at several islands, including Samothrace, Crete and Rhodes, but records no mission there. Mykonos and Santorini, common on cruise programmes, are not Pauline sites. Crete is linked to St. Titus, whom Paul left there. Patmos is the island of St. John, not of Paul.
Source: Acts of the Apostles 16 (NABRE, USCCB): Troas, Neapolis, Philippi and Lydia
