We decided to stay at Claudia's based of course on reviews but also size - nice to have a bit more space - and location.
There are essentially 2 main options in Bergamo: stay in the old (medieval) city or stay in the more recent new town, parts of which are nevertheless still over 100 years old.
Claudia's apartment is in the modern part of Bergamo and although staying in the old city would be very authentic, it's clearly much more crowded; we were there in early November so I can safely assume it must be very crowded in the peak season. However it really doesn't take more than 15-20 minutes to go to the old city, either using the funicular or a short but somewhat steep walk, which we chose.
With hindsight, we made the right decision for us, and I'd stay again at Claudia's in the modern city and go up to the old city for sightseeing as required. Also worth noting there are excellent restaurants near Claudia's and although there are of course a lot of restaurants in the old city, nevertheless one did get a feeling that many were rather touristy.
Finally access from the airport and train/bus station is much easier from the modern section of the city.
As regards the apartment, the photos are representative of what you will find there.