I went to Nervi for a week recently with a one year old. Just outside Genoa, very nice town. Near some lovely places on the Ligurian coast. It's a bit touristy on that stretch but quite pretty. In Genoa there's the maritime museum kids might like, plus a huge aquarium, and the 'city of children and young people' which is kind of hard to explain but good fun. Some nice beach towns nearby too. It's also pastry and focaccia heaven for luches and snacks. Locals were incredibly nice and love kids. Genoa is a pretty short flight as well, and the flight into the airport along the coast is cool.