I personally don't know any 3rd party DB that is focused on quests, sadly. Official Data Base from Lodestone itself might help you on that, though:

https://eu.finalfantasyxiv.com/lodes...uide/db/quest/

It has filters by zones or type of the storyline, whichever is more comfortable to you, and info on the page for a quests says where it can be accepted and if there's anything you need to finish before the quest will be unlocked. The main downside I can think of is that you can't really use it as a to-do list, since there's no option to mark if you did the quest or not.

To compensate it, on lodestone there is now "My Quests" feature you can access from your character info, and it shows all the quests you have completed on a said character:


As such, it will take manual going through it, but you can compare what you've done with what there is in data base going from section to section.