Aetheryte

[Lambdafish]

Cost, however, seems to be an interesting aspect of the whole thing...what is it they use the gil for maintenance wise?

This was addressed in a Duty Commenced episode, it's not a maintenance cost at all. Basically, when the calamity happened, aether travel was crippled and it was a massive problem, so the syndicate of Ul-Dah stepped in to fund the reconstruction of the aethernet. The fee you pay when you teleport is paying off the massive loan that the syndicate gave to the eorzean alliance.