We visited Naples as a single-day trip by train from Sorrento. It's a BIG, grittier-than-most city. It's National Archaeological Museum is full of treasures from Pompeii and elsewhere, truly a world-class sight, in a gorgeous building. We also got pizzas at L'Antica Pizzeria da Michele, the birthplace of pizza, after taking a number at the door and then waiting (about 2 hours) for a table. It was worth the wait, and gave us a chance to stroll the neighborhood, which was pretty grim. Lots of trash, kids throwing glass bottles and breaking them against walls, a slice of Neapolitan life that was a bit uncomfortable. There were 2 of us . . . I wouldn't recommend it for a lone woman, especially at night.
So Naples is worth a visit, but be wary, and I wouldn't personally devote 2 days there unless you had specific things to see or do. If you enjoyed Pompeii, the site of Herculaneum is even closer to Naples, and was buried in the same eruption, It has it's own sights that make it unique and well worth a visit.
If you want a night or 2 in another place, Sorrento is worth considering, but it's a longer train ride from Rome, and you'd change trains in Naples.