There is a shuttle bus stop that goes to both Termini Station and Piazza Cavour (near Vatican City) for 6 or 7 euro. When you walk out of the airport, turn right, and walk straight and you will end up at all of the shuttle bus stops. The very first one is called "Sit Bus Shuttle" - I used to live in Rome and used it all the time. I used it again in July when I went back to visit friends. You can book online, but honestly - you really don't need to. You can pay in cash right at the shuttle. Here's their website in English: http://www.sitbusshuttle.com/en/ (FYI - Da Vinci airport is known as Fiumicino).
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There is a shuttle bus stop that goes to both Termini Station and Piazza Cavour (near Vatican City) for 6 or 7 euro. When you walk out of the airport, turn right, and walk straight and you will end up at all of the shuttle bus stops. The very first one is called "Sit Bus Shuttle" - I used to live in Rome and used it all the time. I used it again in July when I went back to visit friends. You can book online, but honestly - you really don't need to. You can pay in cash right at the shuttle. Here's their website in English: http://www.sitbusshuttle.com/en/ (FYI - Da Vinci airport is known as Fiumicino).