it is difficult to find timetables for the connection to the Aeolian islands so you can plan your trip to the islands. So I decided to paste in timetables I can on the harbour on Lipari for you to consult.
I will upload timetables here asap.
Traveling Aeolian islands
prepare your trip wintertime and summertime.
Especcially wintertime, I recommend you to check the meteo for the South Mediterranean around Sicily. BBC shows good maps and the Windfinder app gives you good data for the Islands if you look for Lipari.
The islands are great for trekking wintertime.
If you decide to come to the islands prepare expeccially wintertime to rest maybe a few days on Sicily and to leave the islands a few days before you have a flight back.
Nice sites in Sicily
There a plenty of nice sites on Sicily, like Siracusa and Palermo. But also Milazzo has some nice things to visit, like the marveluous beach on the west side. with views over the islands.
When I leave the islands I always use to leave a day before. You can never be sure in Sicily. I have experienced bus and train strikes, accidents on the motorway and wintertime of course bad weather.
Train to Neaple and boat overnight.
Recent times, I stayed overnight by friends in North Italy and when the meteo looked nice I called Siremar in Neaple and then took the train to Neaple, a cab to the harbour and finally the boat with cabin overnight from Neaple (at about 20.00) passing Capri, Stromboli, Panarea, Salina to arrive recoverend and relaxed to my final destination Lipari. The boat from Neaple is a big one with restaurant, cinema, internet and bars that does not stop for some waves. It takes 2½ hours with train Freccerosse from Milan to Neaple!
Hotels I used on my trip back.
So I used the last years to stay overnight in Catania at summertime e.g. Le Dune at the nice south beach near the airport or the International airport Hotel. I book these hotels with www.booking .com.
International airport Hotel has a nice pool open summertime, a nice restaurant, 400 meter to a supermarket,10 minutes bus to Catania city and 3 minutes hotel buss transfer to the airport.