I am surprised to see Tuscany and northern Italy mentionned here for late October- for someone who wants to avoid winter woolies tbh. Rome or Puglia, yes, or Amalfi coast.
I'd go for Sicily too, my favourite region being Ortigia in the SW or Cefalu in the NE.
Or Seville, yes, with a trip to Cordoba (by train, its great).
Be warned though that the Amalfi coast is likely to see spells of very heavy rain at the end of October, the last time I was there the road between Sorrento and Amalfi was closed, which happens quite often in the winter months, and I thought Sorrento itself was a bit dull (apologies to Sorrento fans). The temperature in Florence averages about 18 degrees by the very end of October, but there’s so much to see even if it does rain that if you do get a wet day you won’t be bored - and the autumn markets in Tuscany are amazing. I don’t know Puglia, I’d agree about Rome, although I do prefer Florence, it’s not so full of traffic, so nicer to walk round. Rhodes is also a great choice. Wish I was going myself!