Head to Pompeii or Herculaneum to view the archaeological remains, or “scavi”, of Roman cities destroyed by the eruption of Mount Vesuvius in 79AD. 

TO GET TO HERCULANEUM/POMPEII 

At Napoli Centrale train station, follow the BLUE signs saying CIRCUMVESUVIANA. They will take you to a lower concourse walkway with shops on either side. Follow this walkway to the end where you'll come to the Circumvesuviana ticket office and buy two tickets (one for your outbound journey and one for inbound). A single ticket to Herculaneum costs 2.20 euro. Pompeii is slightly more as it is further out. 

Tickets 'validate' as you insert into the barrier and retrieve them on the other side after passing through the barriers. You'll then go down some stairs to the platform. Trains run ever half hour and can be very crowded.  Be sure and guard your valuables. Don't leave wallets in back pockets and if you're carrying a backpack, hold it in front of you.  This is simple common sense to guard against pickpocketing.

The timetable Naples to Sorrento (via Herculaneum and Pompeii) is here

 http://www.eavsrl.it/web/sites/defaul...

It will be helpful to download and print this timetable. There are NO station announcements on the train itself and very few maps on the walls of the train cars. If the train is crowded it will be very difficult to see these maps so print a copy of the timetable and count the stops until yours arrives.

For the HERCULANEUM site, in the town of Ercolano, be sure to get off at the “Ercolano Scavi” stop, then walk downhill for about 1 km (½ mile).

For POMPEII, use the “ Pompeii Scavi, Villa dei Misteri” stop, and walk approximately 100 meters to the Porta Marina entrance.

Guided tours can be taken from the Porta Marina ticket office. 10 euro per person and they wait until groups of at least 10 have assembled. The audio guide is out of date and not recommended.

If needed, both sites offer facilities for the storage of your luggage (baggage) at their main entrances - as marked with yellow suitcase symbols on the official maps:

P: http://www.pompeiisites.org/allegati/...

H: http://www.pompeiisites.org/allegati/...

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Alternatively, there's the option of using a Naples taxi for your excursion, with the city's Flat Fare system offering 3 choices:

- round trip to Herculaneum - including a 2 hour wait while you visit the site - €70

- ditto, but to Pompei - €90

- or a visit that covers both sites, with 3 hours waiting time to be split between the two however you prefer - €130

See the "How much should a typical taxi ride cost?" entry for more details