we would like to spend a week in Sicily in early October. Looking for suggestions of what to see, where to go. Thanks!
Sicilia is huge. What kinds of things are you interested in? You may want to choose one or two areas.
Greek art, architecture: Agrigento, Segesta, Selinunte
Roman art: villa Romana del Casale near Piazza Armerina
Christian art: Cefalu cathedral, Palatine Chapel in Palermo, Monreale cathedral
Hill towns: Piazza Armerina, Erice, Enna, Noto, Ragusa
Nature: Mount Etna, Taormina, Stromboli, many national and regional parks and preserves
Beaches: Taormina, Cefalu, Mondello, almost anywhere along the coastline
Food and wine: everywhere
One place to get ideas is to copy the route of Rick's Sicily guided tour. Rick does not publish a guidebook for the island but the Michelin Green Guide and Lonely Planet guidebooks that are specific just to Sicily are two that we like.
I went to Sicily in spring 2014, and my VERY detailed trip report is here: https://community.ricksteves.com/travel-forum/trip-reports/sicily-palermo-caltanisetta-siracusa-taormina
Addendum for after you read the report: My friend who took the trip with me just went back with his husband. He enjoyed our trip enough to basically duplicate it with only minor modifications, and they both enjoyed it this time too. The major change was the for a GPS, this time he took a TomTom. It worked better than the Garmin, in that it knew the roads around Silvia's agriturismo near Caltanisetta (he said it was a strange sensation to drive around there without getting lost!).
Are you planning to rent a car? Unlike Harold's friend, I didn't have much difficulty driving around without GPS, but it would have helped in a couple of places. Without a car, you can still see enough to fill up a week - as Zoe hinted, there is a great deal to enjoy on this large island, but you'll be more limited in your choices. Public transportation is not that great (infrequent service, some slow roads) so going far afield without a car can use up a lot of time.
You will want to use either the Palermo or Catania airport depending on which side of the island you decide to visit. You could also fly into one and out of the other, seeing a bit of each side. You should plan what you want to see and do before buying plane tickets, but you should also take into account where you'll be flying from into and out of Sicily.
Chani, where have you been?!
About public transportation, Sundays are not good days for taking buses to the smaller towns. Trust me.
Only spent a few days in Sicily and very much want to go back to see more! next time; however, I would look into car rental. We wasted so much time waiting for trains and getting from place to place. Unlike the mainland, trains are not as prevalent or cover as much territory. We couldn't get to the final town on our last day and ended up sleeping in the Palermo airport....We did enjoy the Valley of Temples in Agrigento and would recommend a stop there.
We just got back from spending 10 days in Sicily ( Taormina, Cefalu, and Palermo). Taormina is beautiful and on a hillside. You can experience the whole town on foot. You will have to take a taxi( 15 EUROS)or public bus(1.90/per person EUROS) from the train station to the city center, as it sits down below the city of Taormina. We took an all day tour of Mt. Etna with Etna Experience (78 EUROS per adult) and it was worth every penny. It even included a 3 course lunch with 3 different wines at a Etna winery. Cefalu is on the northern coast and a beach location. The sand is smooth and the town is quiet and relaxing at night. Palermo is busy and alot like large US cities. We stayed in the La Kalsa area and walked everywhere ( the Vucciria and Ballaro markets, the city center, and to the port). The street food in Palermo is amazing and fabulous. One week in Sicily is not much time. You will have to pick just a few places or towns/cities to visit.
You can take a bus or elevator from the train station as well. Taxi will be faster, more comfortable.