Italy Itinerary Help: Train travel planning

Hi! Traveling to Italy at the end of April and I'm working on the itinerary. We're hoping to definitely go to Rome, Perugia, and Florence, all via train. I'm wondering what other cities would make the most logistical/efficient sense to visit in terms of train travel, trying to avoid large amounts of travel time or lots of transfers. We'll likely fly into Rome, and train to Perugia then Florence. Are there any spots along those routes or further past Florence we should see? We're open to anything! We're into architecture, arts, crafts, gardens, lovely scenery, shopping, and things of the like. Any recs?