Nice apartment, nice host. Would definitely stay here again. We didn't have any issues with the stairs leading up the bed (as some other reviews stated). However, it might get warm up there in summer (we stayed in January), depending on the AC possibilities. The bed was comfy, but relatively hard (as many other beds in Italy).
While we stayed there, there was quite som noise from the street (mostly just people, no cars) and construction going on. Of course, we cannot be sure if the host knew about the construction, and it was not constant, but be aware that the apartment is located in a busy part of the center. However, this of course also means that it is super close to many of the sights (the Duomo is right around the corner) and everything you need is in the vicinity, which is great.