Lipari
It is the biggest Aeolian island and features a great variety of restaurants, bars, shops but also monuments, such as the cathedral or museums. As in Salina, you can rent a car or scooter to tour the island. In the pumice quarry you will enjoy white sand and crystal-clear water where you can anchor your boat.
In Lipari you will find several floating docks, but the safest port in case of bad weather is Porto Pignataro.