The Pepper Room is a good value and right in the city center. I have lived in Florence before in previous years so I knew what to expect when living in the ancient city center in an old apartment.
I would describe the stay in the Pepper Room too be very comfortable and accurate as it is listed but I would point out a few things for visitors who are coming to Italy for the first time. First, it's a very very old building, as are ALL the buildings in the city center. You may experience certain quirks like the hot water in the shower is inconsistent as is the water pressure but most all places in the old city are like that and it's perfectly useable, one just need be a little open and patient.
Another point is the window faces out to the street. The old city of Florence has tight alley streets and at night when people are walking down the street and talking yes you will hear the. Sometimes people will be a little loud because the buildings are so close together. Most any apartment will be like this. If you are easily frustrated by a little noise then a hotel may be better for you. I sleep with earplugs anyway and I was just fine and I am normally a light sleeper.
The door to the Pepper Room is adjacent to another bedroom, which is no big deal of course but you may have a neighbor who is not so quiet like we had on our last night, which can be frustrating. That is the only thing we found disturbing and that's the risk you take when staying anyplace that is a shared space.
Some great things about the apartment though are the location is fantastic being walking distance from the train station and anything else you'd want to see. Just perfect location! Also the apartment is supplied with basic toiletries and there is coffee and tea and biscuits in the kitchen. Everything is very clean and tidy. Good wifi.
The only negative for the Pepper Room is you have to share a bathroom with the adjacent bedroom but that is known upfront so no surprise, just hopefully you have a good neighbor. In general if you don't mind a shared bathroom, the Pepper Room is a great affordable option in Florence. Also just downstairs is a market to buy food and drinks so in terms of convenience it's really great.