We don't have children, and pre-covid did several holidays in Sep/Oct. Less crowds and still warm enough to swim. Some places were a little cooler at night, so a cardigan is handy. I can't recall the exact dates/temp though.
Majorca. We stayed in the city and 1 highlight was a day trip on a small gauge train to Soller. I actually wished we'd stayed in Soller, because there was a beach and marina, lovely restaurants, a market the day we went and just more of a holiday vibe than the city.
Malaga. We've stayed in the 'city' many times but never the coastal resorts. the city has lots to see and do, a beach, boardwalk and a mix of locals and tourists.
Rethymon in Crete. We flew in/out from Heraklion airport, but Rethymon is almost in the centre of the island, so can also be reach from Chania airport. I've heard good things about Chania too, but never visited. Nice harbour and walkabout town. Plenty of restaurants. We caught a bus to Heraklion to see the museum and Knossos- if you are into history.
Sicily- but might still be hot. We were there 2 weeks. Flew into Palermo, few days there. Modella beach was a local bus trip away for the day, otherwise along the coast is Cefalu which has good reviews. We also went to Agrigento, Catania and Syracuse. Taormina also has good reviews, but we didn't get there due to a rumbling Etna!