Lived there for 3 years..if you really want quilt quality fabric you won't find it in Italy!
You can find some cotton flat folds at local markets, and some better cottons at a dress maker's shop, but they don't have quilt shops!
Not sure where you will be in Italy but Ercolano is the Garment/Costuming district and I found you could buy scrap bags of various fabrics/yarns/trims there pretty reasonable. Of course that was back when the $ to Lire was really good...now that the $ is in the toilet and Euro reigns, things are not cheap in Europe!