Panarea is one of Italy's Aeolian Islands, off the coast of Sicily.
Panarea is reached by boats from Lipari, largest of the Aeolians. The SIREMAR line  offers fast hydrofoils, which are preferable to slower ferries, particularly since you'll have no need for a car.
It's a small island, and you can get around quite well by foot.
- Panarea has excellent, scenic beaches. Some offer views across the sea to the volcano-island of Stromboli; you can see ash and steam clouds from the volcano's frequent, small eruptions.
- If a hiker, check out the Bronze Age ruins a short-to-medium (5-km round trip) walk from the dock, at the entrance to a nature reserve. No amenities, and the ruins are largely unexcavated; you'll be reminded more of the austere sites of the American Southwest than of the glories of Rome.