I just read this thread for the first time to find that all previous 6 posts mentioned only the island of Vulcano, so I would be glad to add my experience on 2 more islands: Lipari and Stromboli. 

Toward the end of my 2 month-long trip to Europe in summer 2012 I took a ferry from Milazzo to the city of Lipari (on the island of Lipari), which is considered to be the capital of Isole Eolie, and stayed there for 2 nights. In the evening when I arrived, I booked a volcano-viewing tour to Stromboli in the following day. 

Beside this tour, another reason I stayed somewhat longer in the Isole Eolie was because I was sort of looking for an ideal island in the Med, an island more developed than Greek islands but less developed than Capri, and, knowing nothing about Isole Eolie, I thought one of the 7 islands could be it. 

I do remember walking around in the city of Lipari but do not remember what I saw besides souvenir shops in the center, so, I probably did not see much. 

Anyway, the tour, which lasted for several hours and with perhaps 15 participants onboard a small boat, first took us to an underwater volcano near Stromboli where you could see bubbles coming up to the surface of water and where we were allowed to swim out of the boat in the warmer water due to the volcano. 

Then we arrived in the island of Stromboli and climbed up to the top of the island / mountain. I believe the way up actually took us about 3 hours. By the time we arrived on top, it was somewhat dark. The idea was that the darkness allowed us to see the fireworks from the volcano more clearly. Unfortunately, however, the day/evening did not have as much volcanic activity as the previous day, or so we were told. I also remember having a very difficult time trying to capture the moment on pboto when the various volcanic holes spewed up the lava high, so we did see something a little more exciting than what this photo shows. But it was certainly nothing compared to what happened just recently at the Hawaiian Volcano WHS. Volcanic activities are as elusive as Aurora Borealis. 

I believe some people do live on the island of Stromboli, and there were a few gelateria / cafes / restaurants near the dock, but I don't remember seeing much more. 

What I do remember from this visit is just an odd happening: When I left my hotel in Lipari for the tour in the morning, I left my laundry in my room for a maid, and when I returned, it was not done. Surprised, I enquired why it wasn't, and it turned out that the maid had thought that I did not leave the correct laundry for her because my dirty clothes were neatly folded and packed in plastic bags, looking like clean clothes.  I must have panicked because I usually do laundry at least once a week when I travel, and it's always difficult to find a way to do it.

And I wasn't sure if these 2 islands were ideal, either. They somehow lacked the Italian charm IMHO.