Past visitors recommended visiting Stromboli volcano (seeing it at night when erupting is extra spectacular), the Museo Archeologico Regionale Eoliano on Lipari, the Scalata al Cratere on Isola ...

The islands do have some hotels and resorts for overnight stays (Lipari is one of the most popular), but they also make for a great daytrip. Check the Liberty Lines website for hydrofoil and ferry ...