I cant talk to the quality of the place, but I can tell you about the size and the neighborhood.
At 50 to 60 euro for a couple, the prices are consistent with the market rates. I cant comment on the higher occupancy rates. The area descriptions like Jokai 2 of 40sm + 20sm I believe means that the apartment is 40 square meters (about 400 sf) on the main level and 20 square meters (200 sf) on the upper level. That means the bedrooms can’t be larger than 10 x 10 feet each. Fairly small. What they have done is cut a tall one story space in half (very common) resulting in two spaces with somewhat low ceiling heights. I am going to guess 6 foot 8 inches to 7 feet clear on the bottom level and maybe 6 feet and a few inches more on the second level. That’s how these generally lay out. All 6 of you, if you fill it, will be sharing one bathroom (probably on the bottom floor) and each person will have an area of about 8 feet by 8 feet in the living area/kitchen/bathroom area. Even though they advertise for 6, I wouldn’t put more than 3 or 4 in each of these. It also means that the apartments are either on the ground floor or the floor just above ground (in most instances) as that’s where the higher ceiling heights were found in these old buildings.
It appears that the apartments are on Jókai tér. A “tér” is a square and this one is sort of pretty. Like the description says, the square is right off Andrassy ut (Avenue). Andrassy is the street that the French modeled the Champs-Élysées after (or was it the other way around?). It’s a great avenue to walk in the evenings. On the opposite side of Andrassy ut is Liszt Ferenc tér which is lined with tourist restaurants and tourist bars. Some good like Menza’s most not so good. But its very close to the Oktogon which is a major transit intersection. From the Oktogon you can reach most of the tourist sites in Budapest with ease. You could in theory walk to the M1 metro stop at 9 in the evening and in under 5 minutes be a block off the Danube eating a pasty at the Café Gerbeaud.
The Opera House and the Operett Theater and the Liszt Academy of Music are all within a few minutes of this location. So if you like theater and music you couldn’t do much better.
You are also a fairly short walk from the old Jewish District which is among my favorite in town. Basically not a bad location. Most locations between Deák Ferenc tér and the Oktogon in one direction and Andrassy ut and Dobb utca in the other direction are going to serve a first time visitor well; with a preference to being closer to Deák Ferenc tér. We have spent our time in Budapest over the last dozen years in the same general location, although closer to the Opera House.