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, 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!