All these are places we went in Sep or Oct. We don't have children and Sep is cooler and less crowds!
Sicily. Flew into Palermo- markets, catacombs, parks, museums. Bus trip from Palermo to Modello beach for the day which has lots of lovely cafes. Then got a train to Agrigento. The ruins look like the Parthenon and the museum has all the artifacts. Then got a bus to Catania. The seafood and fresh food markets were amazing! We did a day trip to Syracuse. We'd read good things about Taormina, but Etna was rumbling so we did other things.
Pompeii! Someone asked we why we'd go there and I said 'why not?'. Flew into Naples. From there, we got the local train to both Pompeii and Herculaneum. All the artifcacts are also in the museum there. Stayed 3 days, then caught a fast train to Rome. Sorento is another option but we didnt stay there.
Rethymon in Crete. Easy town to walk around. Caught a bus to Heraklion to see Knossos and the museum. I've read Chania is nice too.
Malaga city- not the beach resorts along the coast. A mix of locals and some tourists, but a working town. Great restaurants. Easy to walk around, a castle, Picasso museum, beach with a boardwalk that goes for miles, recently renovated port area, cathedral, fresh food market etc. We also did a day train journey to Rhonda to see the famous bridge.