We visit Budapest regularly and mostly stay in the inner city, which is usually noisy but has the cafes and shops and easy public transport. It was a nice change to the Buda side which is quieter and less frantic. The apartment itself is facing an inner courtyard and the noise you get is from the residents. Although we never met Marcus (who lives in England), he was in many ways the most attentive host we have ever encountered; through his emails, instructions and arrangements, and above all, his art that fills the apartment, we felt we have come to know him. Inside the typically dark and somewhat rundown building, the apartment itself is completely updated, bright and spacious with high ceilings. The kitchen is modern and extremely well equipped, the two bathrooms are luxurious.
The apartment is close to several of Buda's famous spas and the newly rebuilt Castle Gardens, through which you can easily ascend (by lift and escalator) to the historic Castle District. There is also a new gallery, musical events, souvenir shops and a superb new restaurant (Bazaar Eclectica) - no doubt there will be many more. But there is a shortage of grocery stores and cafes nearby, and you would have to walk across one of the bridges or take a bus to do some real shopping. (The grocery store in the adjacent building was closed or under renovation, and the shop in the new Gardens is an expensive convenience store for the bus tours.
One of the real bonuses of staying in the apartment was meeting Mark, who lives on the same floor; he is a delightful English expat retired from the movie business and he has turned his place into a set cum props room. On the whole, he and Marcus have made our stay the most memorable we had in Budapest.