It is likely because the area is too laggy, when teleporting into the inn it could be causing some issues on certain machines/internet speeds, causing to many connections to that specific server section that handles the inn.

No one goes to the other cities, so their entrances have zero lag. But everyone is stood outside Uldah Guild as well as in the Adventurers Guild.

I actually prefer this, its located better. The Limsa airship lift is right next to Inn, so that is fast, the Airship to Grid is also at the guild so you walk upstairs and ur right there, but the Uldah one you had to do a big run through all the lag to get to the Inn from the Airship. This position will be better suited for that need when related to the other cities XD