My family (two adults, one 17-year-old) stayed in the apartment from 5-9 July. It was exactly as shown on the website, and was in an excellent location from which to explore Budapest. We were in the city during a heat wave and the air conditioning (heat pumps in both bedrooms and the living room) worked beautifully and made for a very comfortable and enjoyable stay.
The apartment was very clean, comfortable and spacious. It was also quiet, both in terms of the building and general location. Although it's near lots of decent restaurants (we recommend Six -- delicious!) and bakeries, there was little street noise. It was also walkable to many attractions, and was an easy ride on by bus from the train station -- other transit options were also nearby. We used both the trams and underground for attractions that were a bit farther afield.
Denes was an excellent host and very responsive to email, even providing some advice when our daughter became under the weather and we thought we might need to find a medical clinic. The check-in procedure was very easy and smooth. There is a small elevator in the building, which made getting luggage to and from the apartment (on the second floor) very easy.
We highly recommend the apartment for its location, cleanliness, and amenities. We would recommend staying there to any friends and family travelling to Budapest in future.