We had a good stay at Simona's apartment - it is located pretty close to the Bari Centrale, near to a small park and in an authentic Italian building. The place was quiet during the night, which was great for our 1,5 year old baby.
Simona herself was pretty responsive to all of our requests - coming with a delay from the airport, refill of the gas bottle for cooking, assistance when the fuse was down.
One thing to note is the overall height of the apartment - it is around 2 meters, which could be a problem for taller people. Also, the housing is a bit shady, even during a sunny day (this will be great during a hot summer, but a bit chilly in its beginning).