List of Quests with a level cap.

I think I should also point out that these new Training Center quests don't ALWAYS say "Under Level 19", but technically they are, since you're kicked out of that place at Level 20, which makes it impossible to turn in the quests.

On a side note, it would be nice to seperate these quests into each specific job (and race, such as Arans and Cygnus Knights).