I'm loving the game, but I'm struggling to level up now.

I played 1-15 Arcanist in Limsa Lominsa, but then stayed in Ul'dah to become a Thaumaturge. I am now at level 12, and I'm kinda stuck. I can't resume my Limsa Lominsa quests until I am 15, and I really want to just solely level up my THM (turns out having a pet wasn't my type of playstyle). I've done all the hunting logs I can, as well as guildleves, and used the recommendation tool. I've done some FATEs. But now there are no more quests, guildleves, or creatures to add to the log.

I keep running around in places in Thanalan that clearly have some quests. Like the ruins, for example. I'm sure there are quests for there, but I guess you can't do many quests in a starting area other than the one you initially begin in? And if that's the case, how are you supposed to effectively level up new classes?

Thanks for the assistance!