Is it just me or does it sound like Ibaraki has Nasal issues?

playing on the jp server and got a quest that is aquired after the Tiamat,Momo fight I think wants me to do a dungeon but theres no arrow pointing to the objective.

If you're talking about the underground cavern ( the one with the four dungeons in the big cave) then just grab the quests (collect the orbs for those quests in the dungeons) and complete each dungeon (the two dungeons without a quest will have them at the end of the dungeon where you will imediately obtain the quest item from the npcs) and there will be npcs that will give you the required items for the main quest.

nah havent talked to the guy in Yamataikou yet. I managed to figure it out at the JP wiki with the shoddy google translation.