Something that might be neat is the idea that day and night affect the difficulty of some dungeons. See, the circadian rhythms of some animals would dictate that they either enter or leave a cage/dungeon during one part of the day or another. So for instance, bats/keese would be present in a dungeon much more often during the day then at night, when they've left to hunt. So the enemy makeup of an area, inside or out, might change depending on the time of day. This also imparts the player with a very interesting strategic element, wherein they can scale the difficulty of their experience without having to change a setting like 'easy' or 'hard.' If you watched the recent Extra Credits that talks about ways to leave the difficulty in the player's hands, this plays right into it. If they want things to be harder, then they can assail a dungeon when the most powerful enemies are present inside it in significant numbers. if they need to make things easier, they can either leave the dungeon or play a song to shift to day or night. Obviously, I think that the day/night clock should probably lock when you enter a dungeon.
@Shironagi I like that idea, sort of a fairy alarm clock. Though depending on the in-game timer, it would probably be good to have the real time warning be about 2 minutes out. Even better, it would be great if that alarm was non-verbal. For instance, if your companion fairy (or whatever form your companion takes) changed to a certain color and made that urgent tingling noise like in Majora's Mask and flew around you in a circle or something, instead of interrupting whatever you were doing with a text box (which is annoying).