For any successful AAA title, I think taking a break from what you are doing adds a little something extra. Great games that show this are Nintendo's Legend of Zelda. The Archery range is still something I go back to today. Rockstar's GTA V even had a shooting range. Disney/Square Enix has the Gummi flight scenes from planet to planet (whether you liked it or not). List your favorite Mini-Game, what game it was in and a Mini-Game you would like to see in Destiny.
Legend of Zelda:Ocarina of Time - Horse-back Archery Range
I would like to see a shooting range in the tower and a mini-game to run over as many unarmed Dregs as you can in 2:00