Excavate the history of Herculaneum.
At the time of the eruption of Vesuvius in 79AD there were around 5,000 people living the city. Then it was completely covered in volcanic mud (as opposed to the ash of Pompeii) – a fact that meant that its preservation was especially effective. Herculaneum is now a UNESCO World Heritage site.
Since its excavation, the effects of the elements have led to the deterioration of some of the site but there are still wonderful treasures to visit, such as the Villa dei Papyri with its wonderful frescoes, and the thermal baths where the poorer city dwellers, without their own facilities, could wash, have a massage, use the gym and relax in the porticoed gardens.
Allow at least three hours to visit the site (though you could spend much longer).
To arrive, take the Circumvesuviana (which runs from Naples to Sorrento) to Ercolano. On arrival you will find signposts to the site.