Be sure to speak with the denizens of Waking Sands and Rising Stones between major plot stuffs too. They will make silly or often relevant comments about current happenings.
Uncertain how new to FF14 you may be but by the twelve be certain to do Binding Coils at some point in the time. Especially before post Heavensward for some unique dialogue with certain npcs. Some job quests also open unique dialogue (Dragoon) if they are completed.
For any unaware because this Mia fricken was, the book within inn room called The Unending Journey will show a symbol next to any cutscenes that had unique dialogue so that you can see this later once you finally meet the requirements for that dialogue to appear.