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.
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 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.
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.)
Next perhaps visit the village of Cannetto then time to head to the local beach (pebbles) at Spiaggia Bianca to cool down a little. (There is another beach at Marina Lunga). The remarkably clear seas of Lipari also make it very popular for snorkelling and scuba diving.
Inland there are plenty of opportunites for hiking and exploring including a couple of extinct volcanoes offering more great views out to sea.
The island can be reached by ferry, either from Milazzo on Sicily (26 kilometres) of from other ports in Sicily in Italy and Italy including Palermo and Naples.
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.