Hey @behastie!
I would say… An actor component, attached to the player.
But that’s just me! You could put it so many places! Especially considering it would just be a bunch of variables. You could put it in the Game State, Game Instance…
I’d use one actor that’s your quest board, then when a quest is accepted it moves that over to your player’s actor component (Something like AC_Quests) and have that store all of the data for accepted/completed quests!
Hope that helps! 