While a lot of things are sped up and shrunk down for the sake of making the game enjoyable, I think the general assumption that we're supposed to make is that Hydaelyn is the same size as the planet earth. The maps we have of Eorzea don't give a great idea of where the planetary poles are, so it's difficult to tell just how big the continents we see are - but most probably, it's the intention that the distance between the East and West edges is roughly the same as the distance between Japan and Great Britain. I think we can assume days or weeks of travel by cart or Chocobo between most places in Eorzea, and the boat ride to Kugane likely took months. Even faster vehicles like Airships don't look like they travel nearly as fast as airplanes do.
While not precisely in-game, Alisae's side-story on the Lodestone a while back mentioned that she spent a considerable amount of time traveling with a caravan, and it was clearly implied that this caravan was on the road for days or weeks at a time.
Honestly, it's probably best not to think too hard about it. If pressed, there's likely a LOT of holes you can punch into the story - for example, Hien's nick-of-time arrival to support the siege against Ala Mhigo castle; it's likely that he and his followers were NOT attuned to any Eorzean Aetherite (possible, I suppose, but unlikely), yet they somehow timed their weeks- or months-long journey to arrive just as the Garleans started to mobilize their air force.