Eszter was a very welcoming and accommodating host, even though we arrived late at night. Eszter's apartment is perfect for a couple: there is a bed-sitting room, which is the size of a large hotel room, with a small but very adequate kitchen, and a lovely bathroom. Everything was immaculately clean, and the modern apartment has a lovely cosy feeling from the funky lighting Eszter has put in.
Most importantly, as we visited over the New Year period when the weather was well below freezing, the apartment is well-heated, and we were very pleased to come back to such a warm cosy space.
Other things we were pleased of was the good wifi connection and the hot, powerful shower. For non-Hungarian speakers, note that the only English channel available on the TV is BBC News.
The apartment is very conveniently only a 15min walk up to the Citadella and Liberty statue, so well-placed for sightseeing. It is also a 5min walk from the metro, which we found a very cheap and easy way to get around, even though we don't speak Hungarian.
If you arrive in Budapest on an evening flight like we did and want to get a bottle of wine or snack before turning in, there is a lovely little deli / off-licence which is open late just at he top of the stone steps, just bear left at the top.
Regarding location: the apartment is not too difficult to find, when you know what you are looking for... as you turn off Bartok Bela Utca on to Menesi Utca, bear left as the road curves upwards and turns into Kelenhegyi Lepsco. Walk past the University on your right and you'll see a flight of stone steps going up, which forks both left and right. Keep left, Eszter's apartment is the first building up the steps - look out for the number set back in the garden.
Note that Eszter has three lovely golden retrievers, who are very friendly and well-behaved, and do not come into the apartment, but they do like to sit in the sunny patch in the garden outside the bedroom window, so I would suggest that this isn't for you if you don't like dogs.