No experience of the place at that time, but I tell you a story. I have a dear friend working in Naples since 25 years; but he is from the north of Italy. Once I phoned him that a similar position had opened in Bologna, maybe he could be interested as he would have been quite near to his former home and his old mother. He replied me: "After I have been in Naples so long a time, I can't go back to the north. In my rest day I take the ferry to Procida or Capri, I spend the day there, and off season they are so quaint and quiet. And a bit of sun. No, I can't go back to the northern fogs".
So, probably you will find the place charming in a strange way, but do not think for a minute it will be beach or suntanning time. You will more likely be in need of a light trench. (Today is 68 °F in Capri, and we are still in October even if a cool one.)
Remember that Naples is at the same latitude of New York; Mediterranean climate does not mean tropical climate.