As anyone who has ever planned a family vacation knows, booking a home that satisfies all of your party’s needs is a true art. By the time my parents, brother, and I embarked upon six days in Puglia in September, I had spent hours searching for a home that checked all the boxes. The nonnegotiables: My dad was set on staying in a trullo (the historic, conical stone homes native to the Itria Valley), my mother wanted laundry, and we all wanted a pool. And for me, a former design editor, aesthetics were always critical.

These criteria triangulated to find us at Trullo Giulio , 15 minutes outside of Martina Franca. Our host coordinated with her neighbor, Anna, to meet us at the property after the 90-minute drive from Bari. We could hear Anna’s tiny red farm truck puttering down the road to greet us, which should give you an image of just how rural this part of the region is—nothing but olive trees as far as the eye can see.…