The Davide’s place is just as described. The terrace on the rooftop is a wonderful treat and we enjoyed the Primitivo and burrata surrounded by the sandstone rooftops of Uggiano. The house is located few steps away from the main piazza and next to the church - right next to several cafes, excellent gelateria / pasticceria, fish, meat and fruit / vegetable shops. Rounded up by a great caseficio few hundred meters away (burrata and ricotta), we experienced Uggiano as a foody’s paradise. The prices are about 30-50% lower than in more popular touristic places in the area.
I highly recommend staying at Davide’s if you want to explore the southern Puglia - Gallipoli and Lecce are about hour drive away with many picturesque beaches along the way, Otranto is around the corner, Alimini beaches was our favorite (15 min drive).