So...what was the point of the new inn quest?

[Viritess]

Could someone give me a rundown on how this quest works?

I got the wanted notice, can I sleep in any city for the first part of does it have to be in Ul'dah? because I've yet to see anything from sleeping in my gridanian home.

I belive you need to sleep in Uldah first, then Gridania, Then Limsa. I was told that and when i did so, it popped and went smoothly for me. I had been going to my normal Gridania Inn room and it didnt start.