So, this is a great accommodation. As for silence, I slept so well, there were no noises at all. As for position the neighborhood might feel a little bit unsafe after sunset but nothing happened (but I never came back home too late in the evening).
It is walking distance from the Acropolis, Plaka neighborhood, which is quite beautiful, and from Monastiraki square (underground stop) but I wouldn't recommend walking to the National Archaeological Museum, because the street you might walk by is really busy with cars, and not such a great walk, unless you pass through Psiri neighborhood (another beautiful part ofAthens) and Syntagma square.
You may find that you won't have so much privacy in the terrace because it is right next to another one form an adjacent apartment, and there's only a little short wall to divide the two of them. Moreover other buildings are really close. But if one is used to it there will be no problem at all.
I enjoyed Athens so much, it was my first time there, and this accommodation was all I needed, with quite an impressive view of the Acropolis!
So, thank you Panagiotis and Mary!