Yeah, I would be surprised if you ran out of quests in Thanalan already. I started in Limsa and have actually been holding off going to another city yet because I am constantly finding more stuff to do. Have you opened your hunting log at all? Use that as a way to get exploring the area. If you hover over a mob it will tell you what area they are in and if you finish all mobs in a section of the hunting log it gives nice XP bonuses. Between hunting log, main story, job story and a handful of fates I haven't even touched many side quests and am already at lvl 18.