Unique experiences in Taormina and Siracusa/Ortega.

You could visit an olive oil maker, and taste oils.
We visited a few: we hired a private driver to take us.

Not exactly “off the beaten path”, but…
On Ortigia, I’d recommend taking in a puppet theatre and taking the backstage tour afterwards

Very close by you could also visit the nearby cistern/catacombs/mikveh under S. Filippo Apostolo

When in Taormina some years ago, we took a half-day tour that included some walking / hiking on Mount Etna. It was amazing to me to be on a volcano, and the drive there was gorgeous. Even better, however, were our conversations with our guide. His stories of his experiences in Sicily as the government was focusing on the real-life criminals in Sicily that have so negatively affected life on the island were fascinating (he had joined the police force, after being a teacher, to help in those efforts).

Obviously, visiting Mount Etna is not off the beaten path, but in those areas of Sicily, really, not much that you do will be off the beaten path. But it will still be wonderful and gorgeous.

Not sure if it what you are looking for, but we really enjoyed a trip to Castelmolo a town above Taormina. We simply caught the bus up. We were able to get a seat at the front of the bus and it was quite the ride with some hairpin turns and the driver turning the massive wheel back and forth with her lovely manicured finger nails, talking the whole time.
We toured the town, had a snack and then hiked all the way down. You can catch the bus down too for more excitement, but we enjoyed the hike down.

Like Chris, I recommend seeing a puppet show, which is a Sicilian tradition. It was all in Italian (maybe Siciliani) and they handed out a very long summary of the plot in English. I was confused before I read a quarter of it. The audience was mostly children, we tourist adults were in the very back (it was a small venue) so we could watch the kids as well as the performance. It was great. I didn't take a backstage tour but I had visited a puppet museum in Palermo so I had a good idea of what went into it.

LIsa, How long did it take you to hike back down from Castelmola?

We really enjoyed an Italian Opera performance in Taormina. It was in a small, lovely building — the performers sang arias from a couple of operas— we had a drink on the rooftop. I think this is a summer activity— Google to check on performances while you’re there.

Renee, i can't remember for sure! I think it took longer than we expected. It says it should be 35 minutes, but I"m sure we took at least an hour. I may be including time through both towns though in my memory. It was a lot of downhill, so easy cardio but not so much on the knees!

From Taormina, we did a lovely day drive around the base of Mt. Etna with a stop at a Emilio Sciacca Etna Wine — a small, out of the way, organic winery. The wine, view of Etna and hospitality were all excellent. Would highly recommend. (We also stopped for a tasting with meal at Gambino Winery which had been recommended by the hosts at our accommodation. Gambino is a highly commercialized, crowded and impersonal experience which we regret versus visiting another small winery.)

Sicily is wonderful. Have a great trip!!

I was in Taormina for two weeks at an Italian school and the best day I had was going on a one day tour to Mount Etna with ETNA PEOPLE.
It was actually one of the best days I’ve ever had traveling in all the decades I’ve been traveling

Roberto was our guide and he was wonderful.

Thanks for the great recommendation on the Etna People. I will definitely check it out.

I enjoyed the papyrus museum in Ortigia and was there all by myself when the rest of the town was swarming with tourists. The floor and stairs in the museum was also a sort of separate museum because it was still heavily marked with pathways and arrows and signs from the COVID era --- let's hope these remain just a relic.

I have it on good authority that Renee is a Communist spy...
As for Ortigia, there is an authentic fishermens market at the bottom where one could try the freshest, sweetest ricci di mare (sea urchin) possible--more zinc for your dink.

Bodywork enthusiasts could also book a massage at the funky-boho place just across on the mainland. Excellent value, excellent quality service upstairs off a storefront.
I am done. The Sicilia