A large Roman city that was buried by ash in 79 A.D., Pompeii gives you an idea of the living conditions of Roman citizens at the height of the Empire.  Note that many of the best treasures are now in the Archeological Museum in downtown Naples.  Open every day except New Years, Christmas, and May 1st, Nov-Mar 8:30-5 and Apr-Oct 8:30-7:30 (last admission 1:30 before closing), €11, 081-857-5347.  Consider the ArteCard, which covers admission.

Smaller but better preserved than Pompeii, Herculaneum (Ercolano Scavi) was a resort for wealthy Romans before it was buried under tons of hot mud streaming down from Mount Vesuvius.  Also see Stars & Stripes article.  Same hours and entrance fee as Pompeii; also covered by the ArteCard.  Entrance at 40°48.36'N 14°20.96'E.

Places to Eat Near Herculaneum

Also see Torre Del Greco places, further below under "Places to Eat Near Vesuvius"

• Casa Rossa 1888 Al Vesuvio - Via Vesuvio 42, Ercolano, beautiful view of Gulf of Naples, both seafood and meat specialties, ~€35, 081-777-9763, closed W, rec'd by Alice.
• Viva Lo Re - Corso Resina 261, Ercolano, near Herculaneum archeological site, on the Miglio d'Oro (Golden Mile) of 18th century villas, enoteca with good wine and good food, ~€30, 081-739-0207, closed Mon, Sun eve, Aug, rec'd by Carla Capalbo, Panorama, Gambero Rosso, Osterie d'Italia, L'Espresso, and TCI!
• Cagnano - Via Roma 17, Ercolano, Cadogan rec's this cheap place just up the hill from the Scavi, serving "huge bowlfuls of pasta" including spaghetti alle vongole.
• La Fornacella - Via IV Novembre 90, Ercolano touristy but "pretty good food" says Cadogan, including good value pollo alla cacciatora and pastas, 081-777-4861.
• Pizzeria la Bruna - Via Nazionale 678, Ercolano, pizzeria with private garden rec'd by Frommer's, 081-883-2431.
• Bar deglia Amorini - just across from the ruins, upstairs dining area has some snacks and pizza, rec'd by Cadogan.
• Le Stalle del Generale - Via Diaz 74, Portici, old 1700's palazzo with good food, €35 tasting menu, 081-486-393, dinner only, closed Mon, Tues.
• Vesuvioro - jams and preserves (via Cardano 30, 081-788-8556), Campania Felix - local foods (Via Cimarosa 4, 081-481-183), and Gelateria Gallo - gelato (Corso Garibaldi 34, 081-475-942), all in Portici, rec'd by Carla Capalbo.
• Italia Caffè e Pasticceria - Corso Italia 17, Ercolano, off Via IV Novembre, serves granite, coffee, and cakes, 081-732-1499, rec'd by Cadogan.

You can drive nearly to the summit, hiking the last few hundred meters to see the beautiful view and the smoldering crater...  The area is the National Park of Vesuvius, which is open every day from 9 until two hours before sunset (i.e. as early as 3 PM in the winter and as late as 6:30 PM in the summer). Take the A3 south from Napoli and exit Torre del Greco then follow the signs (which are, unusually for Naples, very frequent and helpful). Parking is €2.50, and adult entrance is €6.50 (as of May 2010). It is also possible to take a bus from Ercolano to the summit parking lot.  See what the weather is like on various webcams.  Wikitravel has a good page on visiting Vesuvius.

These Roman ruins, found in Torre Annuziata on Via Sepolcri, are not as well known as Pompeii and Herculaneum, but are also interesting.  Open same hours as Pompeii, €5.50.  Further south, in Castellemare di Stabia, are the ruins of Stabiae: Villa Arianna and Villa San Marco are near the Via Nocera Circumvesuviana.  To the north, Boscoreale has a museum at Villa Regina.  Villa dei Papiri is another less-known archeological site.

The "Mile of Gold" is a stretch of old palaces beginning, in the north, with the old Royal Palace of Portici.  Since all the rich people wanted to be close to the king in the 18th-19th century, many of them built palaces here.

Pompeii and Herculaneum are both acessible from downtown Naples via the Circumvesuviana (stops "Pompei - Scavi" and "Ercolano" on the line to Sorrento); see the Transportation Page for details.  You'll need a Unicocampania Fascia 2 (Ercolano) or Fascia 3 (Pompei).  Both archeological sites also are (relatively) easy to get to from the A3 highway from Naples towards Salerno.  Vesuvius is accessible via busses from Ercolano, but it is usually cheaper/easier by car.