May, June, and September are the best months on Capri. The weather is warm and settled, the crowds are manageable, and the island has a functioning rhythm beyond tourism. July and August are high season: the Piazzetta is packed by 10am, the funicular queue is long, and the Blue Grotto can have boats queued at the entrance. If you visit in summer, stay overnight — after the last ferry leaves in the late afternoon, the island becomes a different place.
October through April is quiet and cooler. Many restaurants and shops close entirely from November to March. The weather is unpredictable and the Blue Grotto is frequently closed due to rough seas. But for those who want Capri to themselves — and who can handle the chance of rain — the off-season has a genuine appeal that the summer crowds obliterate.