This is one of the best properties I have been to - ever. The apartments are very large and excellent value for money. They are well equipped, very clean, very well maintained. The kitchen appliances are full size (European, not American), not the mini-versions you find in some apartments. You can use many of the facilities of the 5* hotel next door, but those are not free. The sofa's and beds are comfortable, the shower has a thermostatic valve and aircon is effective. Sound insulation with neighbouring rooms is good. The staff are very nice. Be aware that the reception has limited opening hours, but there is a phone number in case of queries.
As for location, although at first sight it seems a little further out from the city centre, it is actually located a few minutes walk from the Jozsef krt, the middle ring road. This is probably the most useful road to be on, since the very frequent and fast 4-6 tram covers all of the Pest side in a semi-circle, and sections of the Buda side too, as well as one of the islands in the Danube.
Aside from that, there is a Spar supermarket also a few minutes from these apartments.
If this is available and within your price range, book this - you won't regret it.