From Rome to Naples is easy, cheap and reliable. Two train companies, Frecciarossa and Italio, offer High-Speed rail services from Rome which takes just over an hour. Booking is easy and simple. You can book directly, both websites have a English option, or through third-party agents like Trainline and Loco2.
You can find more information about rail travel in Italy on the Man in Seat 61’s website.
Note: When travelling on the train in Rome, you MUST validate your ticket at the ticket machines prior to boarding. If you do not, you could get a hefty fine.
If the Pope is in residence, on Sundays at noon, the pope appears at the window to pray and bless the crowd in St Peter’s Square. No ticket is required but expects long lines. We highly recommend you bring water, snacks and a sun-hat, especially during summer as there is a lack of shade.
St. Peter’s Basilica dominated St Peters Square and is a must visit. It is free to enter the main St. Peter’s Basilica, though there are admission fees for a few parts, such as climbing the cupola and the Vatican Treasury. St Peter’s Basilica is open daily, April-Sept 7am-7pm and Oct-March 7am-6pm.
The Vatican Museums are open Monday to Saturday and closed Sundays. There is a charge to enter the museums and you can pre-buy tickets on the Vatican Museums website.
I recommend the Rome Toolkit website which has information on everything you need to know about the Vatican and Rome. https://www.rometoolkit.com/whattodo/vatican_stpeters.htm