I stayed at Matt's place for one night. Matt wasn't there himself but he arranged for his friend to meet me there and help with check-in. The apartment was conveniently located close to the train station. The centro storico was a walking distance away.
The apartment was good all in all. It was hot in Bari though, so the apartment was really hot too (no ac). However, I could sleep the whole night with the balcony doors open and not be too disturbed by the voices outside.
I recommend staying with Matt, especially when it's not as hot as now :)