I was asked this question earlier today and I realized I've just never thought about it until now.
Have I missed a tidbit on this most basic of information somewhere?
The Gil coin is a standard currency throughout all of Eorzea, so I figure it must be something all of the city-states have had in common for a long time. So far, I can't think of anything other than the Twelve, so let's start there. The first suspect is, of course, Nald, the aspect of The Traders that oversees the living's financial fortune. However, the face is to my eyes quite feminine. The 1.0 icon for Gil also shows a reverse side that I can barely make out, but it seems to be a tree. Perhaps then the face is Nophica, goddess of abundance and prosperity? The figure also seems to be wearing a crown that is unlike the one I've seen Nophica wearing in SE's previous artwork - it does, however, look akin to that of the Sultana... It'd be strange for one city-state to make all of the realm's currency in their own ruler's image even when the nations commonly found themselves against one another... but if one city were to do so, it would be Ul'dah...
Any ideas?
EDIT: Mystery solved! See below (Thanks, Community Teams!)