May and June and September and October are the best months. The weather is warm (20–25°C), the sea is swimmable from May onwards, the crowds are manageable, and accommodation is reasonably priced relative to peak season. The spring wildflowers on the slopes above the road are an added bonus in April–May.
July and August are extremely busy. The roads clog with cars and tourist buses, the beaches are packed, and accommodation prices are at their highest. If you must visit in summer, consider staying in Ravello or Atrani rather than Amalfi or Positano — both are less overwhelmed. The evenings are more pleasant than the midday.
November through March is quiet and some places close. The coast in winter light can be beautiful, and the fishing villages have their character back. Rainfall can be heavy, and the occasional closure of the coast road due to rockfall or flooding is a real possibility. Come in December or January if you don't mind taking the risk — you'll have the coast largely to yourself.
The Ravello Festival runs throughout July and August and is a reason to visit if you enjoy classical music on an extraordinary stage.