If you're looking for a place to stay in the heart of Bari, I recommend Melo 48. Housed in a residential building, I stayed at the "standard apartment," but there are also a few other room types available.
First of all, the location is fantastic - within walking distance to the old town, the main shopping street Via Sparano, and the train station. Next, the apartment itself is modern yet cozy that makes you feel at home, super spacious, comfortable, and well-equipped with everything you need. Also - good communication with the host Anna, and an easy self-check-in process.
All in all, I had an extremely positive experience here, and I would definitely book it again!