It's my understanding that Constantinople was not, in fact, founded by St. Andrew. Constantinople was merely a Metropolitan See until the significance of the city increase due to secular movement. Do you have any direct text to gaze upon?
It seems that there are texts in Greek to be gazed upon.....
This is from Halsall at Fordham:
Demetrius Kymenas, deriving his comments from the Thriskeftiki kai Ethiki
Encyclopaedia (Athens 1962-8) sums up the situation as follows:-
It is difficult to say where the legend stops and where reality begins. However, the Apostle Andrew preached in the general area and according to the tradition he ordained the first bishop of Byzantium (Stachys), the first bishop of Nicaea (Drakonteios), the first bishop of Chalkedon (Tychikos), the first bishop of Sinope (Philologos), the first bishop of Thracian Herakliea (Apellis), etc. (He ordained many of the Seventy Apostles as bishops in cities of Asia Minor, Thrace and Greece).
Because the lord of the small city of Byzantium, Xeuxikus, was brutal and a fanatic pagan who used to tie and throw in the sea any Christian who visited his city, Andrew resided in nearby Argyroupolis (later a suburb of Constantinople), and there he stayed for two years during which time he managed to create a Christian community of 2000 people along with their church and episcopate. It is not clear if Stachys is the same person with the one the Apostle Peter calls "dear" in his letter to the Romans, but his memory is celebrated by the Orthodox church on October 31.http://www.fordham.edu/halsall/byzantium/texts/byzpatcp.html
Byzantium, out of which Constantinople sprang, was a small, well-fortified town, occupying most of the territory comprised in the two hills nearest the head of the promontory, and in the level ground at their base. The landward wall started from a point near the present Stamboul custom-house, and reached the ridge of the 2nd hill, a little to the east of the point marked by Chemberli Tash (the column of Constantine). There the principal gate of the town opened upon the Egnatian road. From that gate the wall descended towards the Sea of Marmora, touching the water in the neighbourhood of the Seraglio lighthouse. The Acropolis, enclosing venerated temples, crowned the summit of the first hill, where the Seraglio stands....http://en.metapedia.org/wiki/Constantinople
In the time of Saint Andrew Byzantium was a very busy mercantile and maritime city, full of loose sailors and bad women, and it makes perfect sense that it would have been a place to go and preach the Gospel.