The city of Bari was great. The apartment was very functional and the location was great, just down your stairs and you are in the middle of the historic center with tons of restaurants, bars, shops and an area full of life. As well to enter the apartment, you enter into a little courtyard where it is authentic, i.e. Italians have their homes in these buildings and it's a cool feeling to be located among the locals. I can't recommend the city highly enough, we loved the energy, the the architecture, the people, the food, etc. The apartment as well was very clean, the kitchen was well stocked with all you need to prepare meals, coffee, tea, etc. The shower worked well, there was a washing machine (which we didn't use)The hosts were very prompt, friendly, professional and helpful. However we wouldn't stay again, not because it wasn't functional and well located but because it wasn't anything special which we look for when we travel and while we didn't mind the stairs and access, I think travelers may find the stairs a bit of an issue, they are narrow, steep and there are three flights. Stairs are certainly part of any historic center but if you need easy access and have a lot of luggage look for the first or second floor in a historic area. To make your arrival smoother, ask for detailed directions on how to enter the Historic center (it's a walled city with specific entrances) and walk the couple of blocks to the apartment as at the time of our arrival it wasn't clear how to get there, however we called and they met us promptly (late in the evening by the way) and it was no issue.
In addition, the terrace pictures are what sold me and it wasn't as 'nice' and comfortable as I expected from the pictures, there is no particular view and the furniture wasn't particularly comfortable. Having said that it might be fine for others, we spent more time in the city than in the apartment.
If the price is right for you and competitive and you don't mind the stairs and don't expect too much from the terrace then go for it. The hosts are great, it's super historic and very very well located.