Is it normal....

[SummerSkye]

...to run out of quests and stuff to do in the City (Ul'Dah) at around level 10? I just got level 10 and other than my level 10 job quest, I do not see much else to do there...I assume the game sort of pushes you along to new areas at this point?

[CWaters]

Keep doing your main quests, it will continue the story line and take you to other city's where you can access more classes and crafting guilds.

Yes it pushes you to other areas, at least it has for me up to level 17.

[surrel]

No, you should have more quests to do in Ul'dah even past level 10. Have you explored all of Western and Central Thanalan? I was questing all the way past 15 until I had access to the airship for other areas and I started spending more time doing levequests and FATEs. If you have no more quests in the city, check to see if you have any new quests in Horizon. I can't remember what level those quests started at.

[Reinheart]

Once you progress through main story quest you'll get recommended quest feature from lv10 (after finishing the mainstory lv10 and unlocking the Inn and rest of the goodies)
This will show you all the quests available currently in that area you're in, at default it only loads when you login, but you can go through config and have this display show up everytime you zone to a new area, and it will update when you switch class/job. It will also display all the mobs listed for that current class in hunters log as well, so that should help you progress through your levels

[Whizawk]

It's all about exploration. The main quest facilitates this by causing you to venture out into the surrounding areas, which will then house more quests or small tasks that people ask for.

[DAMNLAMA]

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.