SImone has a great apartment in the middle of Centro Storico, having breakfast on the terrace is really amazing and it's within walking distance from basically all the sights in Naples. The bathroom is a bit tight and you have to pay attention not to flood everything while showering but otherwise the rooms are perfect.
The only negative is that because of the airport's proximity to the city and the seagulls living on the rooftops nights are extremely loud, but I think that's true for all of Naples. Bring earplugs if you want a good nights sleep