The allure of the Aeolian Islands is immemorial. A necklace of seven volcanic peaks, rising from the Mediterranean off the northeastern coast of Sicily, they appear in Homer’s “Odyssey,” where Aeolus, the keeper of the winds, offers generous hospitality to Odysseus and his crew, as well as a fair breeze for their return voyage to Ithaca. Alicudi, Filicudi, Salina, Lipari, Panarea, Stromboli and Vulcano were collectively designated a UNESCO World Heritage site in 2000. Each has a distinctive and intriguingly different personality: Alicudi — where donkeys are the only means of land transportation — and Filicudi are the quietest islands, Salina has become the most fashionable, and Lipari is the largest and busiest. Pretty Panarea is a long-established favorite of moneyed Italians, which makes it a clubby and rather standoffish place, especially for anyone who doesn’t speak the language. The volcanoes in the middle of Stromboli and Vulcano are still active, while all of the islands have steaming fumaroles or thermal waters. Stromboli is also a favorite island for hikers, who ascend as close to the edge of its crater as they dare.