We liked our stay at Ignazio's place. There is some renovation happening in the building, but no actual work going on during our stay. He was kind enough to arrange a bed in the living room for our kid, and he slept comfortably there. The apartment is on the first floor of a small street in a residential area. The sound proofing is quite good and we were not disturbed by any traffic. The area is safe and there a lots of little shops, a supermarket, and it's easy to grab a cornetto and coffee in the morning :-)
Keep in mind this is not close to the old city, Bari Vecchia, or the sea. It's probably a 35 min walk to get to Bari Vecchia, and the area is not very interesting to walk. There's a bus that runs a fairly frequent schedule, and doesn't stop very far from the apartment.