We visited Bolzano one afternoon which is a nice place to explore and has a museum centered around “Ötzi”, the mummy of a man found frozen in the ice from about 3300BC. Other than that we were there for hiking in the mountains so conditions will be quite different when you visit.
I noticed one of the places you’re going in Italy is Puglia. We based in Lecce and spent a few days exploring the region. We found the book “Lonely Planet Puglia & Basilicata” useful in describing Puglia and for planning our visit. It’s about 15 years old but the towns haven’t changed that much (the train times in the book are generally wrong though). We also looked for blogs with stories from travel in Puglia and watched YouTube videos such as walking tours. While planning your time there keep in mind that in rural southern Italy many shops/churches/museums close for the riposo from about 1pm until around 5pm and restaurants close by 2pm. Tourism mainly happens before lunch or in the evenings.