Originally Posted by LHR Tim
NAP could be fun -- bustling, terrifying city (those scooters!).
There's Pompeii (OK cultural, but they may like it). Mumified dead people - kids think that's cool
Hike up Vesuvius (and see it steaminng away!).
Loads of places on coast (Amalfi, Postiano, etc) for water fun.
Oh, and since it is Italy - Gelato
Not to mention the home of pizza and some pretty damn fine other southern Italian food. The Hotel San Francesco al Monte is a great base overlooking the city - part of the city but not at ground zero of where it gets most frenetic. There's a lovely rooftop pool, in case you (and the bambini) need a day of splashing about without the stress of getting to the seaside. Beware if venturing further - Neopolitan driving is quite unique and it can be gridlock between Napoli and Amalfi on the coast road at weekends and / or during high season. You could always consider getting one of the plentiful ferries or hydrofoils to one of the nearby islands.
Bari is also worthwhile - Matera (location for
The Passion of the Christ) is about 80 mins drive from the airport and where you'll get a chance to experience 4-star luxury while staying in a troglodyte cave dwelling.
My vote goes to Napoli for the sheer diversity of available options - not to mention distractions - to keep the kids happy.