At the last time I went to Athens (which was 18th February Saturday), passing by Kapnikarea Church...
I noticed that Georgiadis Patisserie/bakery opened a branch here.
Georgiadis is "the" patisserie/bakery of Varkiza.
In comparison to the shop in Varkiza, the range of items on sale is limited here, but still there are some interesting choices.
I tried pie with Philadelphia and ham.
The quality of the ham was obscure, but the pie crust was very nice.
The shop is no doubt a valid point to pick up your snack when you are in central Athens.
And another newly opened pie shop in central Athens called Chryso.
It is specialized in bougatsa, and except for the bougatsa with semolina custard usual in Athens, they have bougatsa with cheese or bougatsa with spinach.
After the snacking at Georgiadis, my stomak could not afford another pie, but on the next occasion, I would love to.