Were there regional concentrations?
I feel like I've picked up the view that Egypt and Syria were particular hotbeds of Christianity in the 2nd century, but I can't claim a source.
I've heard the city of Rome had a particularly high population of Christians since the 1st century- were other cities in the west home to large number of Christians?
How Christianized was the interior European hinterland compared to the Mediterranean basin by Constantine's Edict?
I've got a bazillion other awkwardly framed questions on this topic, but really any information would be nice.
Antioch in Syria and Alexandria in Egypt are centers of early Christianity. This is a combination of (a) being quite large cities in the 2nd century, (b) being relatively close to the ground zero of Jerusalem, (c) in both cases I suspect relatively high proportions of Jews made the spread of Christianity more feasible (even if it is not Jews who are converting, knowledge of Judaism would form a preliminary basis for conversion).
One of the things to realise is that the answer to some of these questions is not Christian demography, but simply demography. The Roman Empire was more heavily populated and developed in the Eastern half, so that tends to be where you see greater Christian growth. Whereas the West is just not as populated, but wherever you see major population centers, you are going to get more Christians, unless there are mitigating factors.
Lyons is an interesting case, since a large proportion of believers there seemed to have come from Asia Minor.
I have to go to work, but I will answer some more on the topic when I come home, it would be good to discuss studies on Christian demography in the Empire.