In summer, the islands are most populated and can be somewhat claustrophobic (and expensive). Your best bets are May, early June to mid July, and September, when the northern Italians still haven't flocked down from their foggy cities. Off-season visits are relaxing and probably best if you want to appreciate the islands for their beauty. Bear in mind, however, that many businesses and lodgings close for the season at the end of September, and the wind can be bitterly cold in winter.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.