Ports of Lipari, Giardini Naxos, Gythion, Monemvasia - Shore Excursions or On your Own?

Lonely Planet guidebooks have some coverage of these towns. You might want to buy single chapters as printable PDFs, for instance for Taormina and Lipari at http://shop.lonelyplanet.com/italy/sicily-travel-guide-6/. When I visited Lipari for a couple of nights, I was happy just visiting the main town, plus boat ride around the island (but your cruise will give you enough of that scenery).

You should determine what you really want to see.

Lipari is a very pleasant town, with an interesting small archeology museum (rich in Greek pottery, IMO). Boat trips leave Lipari for the other Eolian islands, notably that of Vulcano, Panarea and Stromboli. These boats are not very big. So, if meandering Lipari would be sufficient for you, then you do not need an excursion. However, if a boat trip appeals, then I would definitely book it as a shore excursion, as spaces on these boats will be limited. I spent an enjoyable couple of days on Lipari.

Taormina is lovely for a leisurely day, with a well-preserved Greek amphitheater that you can visit on your own. Pleasant streets, shops, cafes and restaurants can keep you happily busy the whole day. There is good bus service up the hill from Giardini Naxos. So, again, no excursion needed if Taormina is enough for you (unless you sign up for a walking tour). If the prospect of seeing Mount Etna up close appeals more, then book a shore excursion and pick one that will combine a stop at one of the wineries in the area.

Given Nomemvasia's rich history, I think that you should plan on taking a walking tour - especially for visiting the upper half's old Byzantine settlement (shore excursion or private). Again, a very nice small town in its own right.

I know nothing of Gythion. You certainly picked a cruise with a very pleasant itinerary!!

You will be able to see Mount Etna in the distance from Taormina, and Stromboli from Lipari. If you decide to take a ferry to Stromboli or the other islands nearby, check the schedules carefully to be sure you'll get back to the ship on time.

Lipari has a nice beach a ten-minute bus ride from the main town. The beach at Taormina is pebbly/rocky.

I think Lipari and Taormina can be done on your own if you do a little research beforehand to be sure you see the things that interest you.

First of all, this newsboard doesn't have a lot a cruisers. You might want to post elsewhere as well. Is this your first cruise? If so, I recommend that you bite the bullet and buy the cruise's own excursions. You'll gain experience that may let you branch out with individual excursions on a later cruise.

To start, ports in the Mediterranean are affected by weather. We visited Monemvasia with Windstar when the ship couldn't get into Mykonos because of wind. So pre-ordered Windstar excursions in Mykonos were automatically cancelled with no cost to us.

When we went on another Windstar cruise, in Central America, it happened that our Windstar bus with guide (I think it was to Copán in Honduras) was delayed returning (from a very, very long drive). The ship had in fact moved to a different section of the port city, not just to a nearby dock. But because we were on an (very expensive) Windstar excursion, not only did the boat wait for us before departing, it was the guide on the bus's problem to locate and find the ship. Do you want to be negotiating that with a cab driver who can barely speak English, and might have a discharged cellphone?

Finally, your research is not working right. Monemvasia is not some hideous "cruise port" with a mall of Armani-knock-off shops and a beach filled with shiny Margarita bars. There's nothing there except a magnificent medieval city on the rocks and rocky hillside. Not even a taxicab stand. It's a superb destination all by itself. Besides actual history, it features in books like the Aubrey-Maturin series by Patrick O'Brien. We happen to love medieval cities, but our pleasant memories of the less-than full-day stop in Monemvasia are perhaps colored by how seasick we were the night before we landed. We sort of kissed the ground! AFAIR, they gave us a free walking tour of Monemvasia, followed by free time to explore the clean, pretty, and almost deserted town. It was wonderful, but I wish I'd researched the (unexpected) destination in advance. There weren't even many souvenir stores open. It was like dropping down into history. I don't remember any food opportunities.
Edit: One reason the Copán excursion was expensive is that it included a cruise-ship quality lunch in the middle of a full day expedition. You might say, why should I have a catered buffet, on "their" schedule, when I already "paid" for lunch on the ship? I'd ask, do you want to risk R-O-S from a cart in a remote monument, in a developing country? I know people who got sick on R-O-S in New York City.