The best time to visit Naples would be April or May. Being in southern Italy, the city is usually warm, although the tiny alleys keep you in the shade most of the time. April and May would be warm enough and still relatively tourist-free (except during Easter). Average temperatures are around 22°C /71°F and 12°C /53°F. Summer (June - August) is the high tourist season, so the prices would be steeper, but Naples is not a tourist heavyweight like Rome or Venice, so the crowds won't be horrendous. Summer also gives you the chance to visit the nearby islands and have a beach day at Capri or somewhere around the Amalfi coast. Average temperatures are around 30°C /86°F and 20°C /68°F. Winters are mild for a European city. The average daily temperatures are around 14°C /57°F during the day and go down to about 5°C /42°F in the night.