So now what?

[Niwashi]

You can visit the two cities in either order. The quest text makes it sound like you have to do one first, but it also says something like "Such and such city is supposed to have their ceremony first, but you never know, it could be delayed," which is the lore explanation for choosing which ceremony/city you see first.

You're thinking of the quest where you attend the various remembrance ceremonies (just before choosing which Grand Company to join). That one lets you do it in any order. The Envoy quest doesn't let you choose destinations. You board the airship and it takes you to where the quest needs you to go next, without giving any choice of destinations. (You don't get the airship pass and the ability to travel wherever you wish until the Envoy quest is completed.)

[Bixby]

You're thinking of the quest where you attend the various remembrance ceremonies (just before choosing which Grand Company to join). That one lets you do it in any order. The Envoy quest doesn't let you choose destinations. You board the airship and it takes you to where the quest needs you to go next, without giving any choice of destinations. (You don't get the airship pass and the ability to travel wherever you wish until the Envoy quest is completed.)

Ooooh, right. Nevahmoind.

[Felis]

I've gotten my Lancer to lvl. 16, been made Gridania's envoy and got the airship pass, visited the other two cities to confer with their leaders, and I've even been to Vesper bay to learn how to dye my gear. So now what do I do?

Go back to Uldah where you did your last storyquest and accept the next storquest, if you didn't see it. It lead you to your first dungeon run.

[Kaeda_Valentyne]

It will pick up in Ul'dah.
Go to: Steps of Thal Upper { like your going to take the lift to the air ship}
I think the aethernet you want is called The Chamber of Rule
Than head south to the Royal Promenade. A guy should be standing by the door to give you the main quest. It will send you to Limsa.