First time visiting Sicily, can you suggest itinerary for east coast?

Our trip to Sicily is coming up in a few months, but as for flights, Delta has a direct seasonal route from JFK to Catania. United is direct seasonally from EWR into Palermo. If you are interested in the eastern side of the island it might be best to look into the round-trip to Catania. To minimize locations, maybe heading straight to Ortigia for a few days and then heading back towards Etna wrapping up in Catania would work. We are renting a car so I did not look into public transit, but I know many members have recommended buses over trains in Sicily. Given the size of your group, it might even be possible to hire a driver with a can to move between primary locations. Part of our trip overlaps with one of the RS tours so his recommended vendors were typically unavailable when I reached out, but we helpful with recommendations if you do opt for a driver.

There is rail service down the east cost of Sicily, albeit not particularly fast or frequent. I used a mixture of trains and buses to reach the Baroque towns like Noto, depending on which schedules were more convenient.

The Catania Airport is the busiest one in Sicily, so if you end up needing to connect somewhere in Europe, you may have more options using Catania. Full disclosure: On those rare occasions when Mt. Etna blows its top, flights into and out of Catania can be affected.

For your time frame, I'd want to manage this trip with just two bases. One would be in Ortygia. For the northern base, keep in mind that picturesque Taormina is built on the side of a hill. The train station is down below in Giardini Naxos. Every trip to or from Taormina requires a bus ride up or down (or there's a lift, but the location may not be ideal). This situation extends the travel time required for day trips. The town itself is also necessarily hilly and would not be my choice for folks with limited mobility. I'm not a beach person, so I cannot make a suggestion from that perspective.

Agree that you should use Catania airport for these places. No point going to Palermo unless you want to see Palermo. If you want to avoid over touristed spots don’t go to Taormina or Ortigia (actually I think you should visit them, but I found a couple hours in each of them to be sufficient.). I think Catania, while definitely second to Palermo in tourist attractions, is an underrated city. Our tour spent several nights in central Catania and I liked it a lot. Very walkable, some interesting sights, not too touristy, nice places to eat. All the places you mention are within daytrip range of Catania (well, not sure about Noto).

We also stayed in Catania as a base on the east side of Sicily (Liberty Hotel) and used car service to take us everywhere (mainly Sunny Sicily). The day trip to see the mosaics at the Roman villa and to see the beautiful ceramics of Caltagirone was a highlight. You can easily visit Taormina and Mt Etna from Catania. We used car service to transfer to Palermo with a stop at the Valley of the Temples so as not to waste a day, but we didn’t have time to see Syracuse or Noto. The service at the Liberty Hotel in Catania was superb. Although it may be a bit rough around the edges, we felt safe walking around.

Our group stayed at Una Palace Hotel in Catania. Right on the main artery of the city, nothing “rough” around there, great restaurants within a few blocks, nice park across the street. If you have any interest in World War II Catania has a very good museum about that time in Sicily, which is a unique site compared to the churches, temples etc elsewhere in the island (which are great, don’t get me wrong). I think two of what I think are the best three sites in Sicily (Monreale and Agrigento) are a bit far from an east coast itinerary, but the third is the Roman villa at Piazza Armerina which may be possible for you.

We also enjoyed our 3 nights in Catania and wished we taken our 3 nights in Ortigia and given them to Catania and Palermo even though we are not city people.

You didn't ask this, but after spending a total of 6 weeks in Sicily, and I had to choose one place to spend 8 days, I would not hesitate in choosing Palermo (including Monreale).