Ripley is Steven Zaillian's black and white Netflix series (2024) based on Patricia Highsmith's novel: Andrew Scott plays Tom Ripley, a small-time con man sent to Italy to bring home a rich man's son, Dickie Greenleaf. Tom is soon drawn into Dickie's life. Start in Atrani on the Amalfi Coast, Dickie's village: the bus leaves Tom below the church of Santa Maria Maddalena, and the little square and the beach are a few steps away.
Group the rest by city. In Naples, see Caravaggio at the Pio Monte della Misericordia and the chapel at Santa Maria la Nova that plays a Roman church. In Rome, walk from the Hotel Hassler above the Spanish Steps to San Luigi dei Francesi and Ponte Sant'Angelo, then the Borgia Steps in Monti; take a bus out to Porta San Sebastiano and the Parco degli Acquedotti. Sanremo was filmed at the pier in Anzio, a train ride from Rome. In Venice, St Mark's Square, the Hotel Danieli and Tom's Palazzo Contarini Polignac are all on the water.
Palermo is a separate trip: the Oratory of San Lorenzo is a flight or night ferry from Naples. Dickie's villa was filmed on Capri in a private house and is not listed. Churches and museums have their own hours, so check before you go, and the Venetian palazzo can only be seen from outside.