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The island of Lipari (and the town bearing the same name) is the largest of the Aeolian Islands (also known as the Lipari Islands, to confuse things further!). The Aeolian Islands are off the north-east coast of Sicily.
The easiest way to get to Lipari is to take a ferry from Milazzo on the north coast of Sicily.
Unlike some of the neighbouring islands (especialy Vulcano and Stromboli), Lipari itself doesn't feature an active volcano. What it does offer is some great scenery, a selection of beaches, and the liveliest town to be found on the islands - Lipari is active late into the night (in the summer) and has a very wide selection of bars and restaurants.
Lipari town is centred around a large fortified castle, overlooked from Piazza Mazzini and built by the Spaniards in the 16th century and very interesting to explore. Within the citadel there are also archeological sites covering a large part of the span of the occupied life of the island - some of the artifacts unearthed can be seen in the interesting museum.
There are also some churches of note in Lipari: the 17th century Church of Santa Caterina is within the walled city, also the 18th century Church of Addolorata. Lipari's Cathedral of Saint Bartholomew has very ancient roots (towards the end of the Roman Empire) and was consecrated in the 12th century. Note particularly the arcaded exterior with its decorated pillars. It also has a cloister dating back to Norman times.
Take the time out from exploring the town itself to visit the Archaeology Museum in Lipari which has an extensive range of artefacts to explain the (very) long history of the islands, dating back some 6000 years, from both within Lipari itself and the surrounding region. It is very interesting and found within the citadel. (It also has a large collection of obsidian, the curious glasslike volcanic rock which has long been an important part of the local economy.)
As the citadel sits up above the town you also get some great views over the island and the sea from here!
Next perhaps visit the village of Cannetto and its beach (pebbles) or go a bit further to the sandy beach at Spiaggia Bianca to cool down a little. The remarkably clear seas of Lipari also make it very popular for snorkelling and scuba diving. You will need to take the bus, a taxi or do a boat tour to explore the island unless you brought your car over on the ferry.
Inland there are plenty of opportunites for hiking and exploring including a couple of extinct volcanoes offering more great views out to sea. The tourist information office on Corso Vittorio Emanuel II in the town centre can provide you with maps.
Lipari also acts as the 'hub' for exploring the quieter islands with ferries leaving from the Marina Corta harbour at Lipari to all the other islands.
Places to visit nearby
Lipari is the liveliest of the islands but Panarea is the most chic and attacks both Hollywood filmstars and the luxury yacht crowd as well as tourists wanting to enjoy the lovely scenery. A guided walk up to Stromboli's active volcano crater or a night time cruise around the island is an experience not to be missed.