I've answered your questions below.

Quote Originally Posted by flaco View Post
- I've explored every part of La Noscea, mostly by running for my life from monsters that where 20+ levels above me (Lv. 12!)

Quote Originally Posted by REDace0
You are awesome for doing this. Did you know there's an achievement for attuning to every node and gate in the current Eorzea that will be going away?
A.) How soon should one leave their home-city (In my case, Limsa Lominsa) and travel to the other city-states?

B.) If I do make it to (whatever city-state,) will I miss out on levequests, or will there be begginer level levequests in that city as well?

Quote Originally Posted by REDace0
You're free to at any time. Every city currently in the game has a guildleve counter and a mix of similarly leveled content. Most players are in Ul'dah, and the main scenario will send you there at level 20. For Limsa to Ul'dah, take the ferry from the dock in the west part of the city's lower level, then follow the road east until it forks. Check your map at this point; Ul'dah should be a short walk south. To continue on to Gridania, follow the road further east and then north. You'll enter the forest at some point. Stay on the road and you should be ok, but it's a farther walk again than Ul'dah.

You could also take the airships.