Some I haven't seen in ARR that I'd like to see are:

-Get to point A to point B without being caught by enemies or setting off any alarms or traps.

-Get godlike powers and be able to completely destroy hordes of enemies. Instance battle, of course. Maybe one of the Twelve can lend your their power to protect a special NPC or something along those lines. I know it's just killing, but to feel like an absolute badass for one quest would be cool. More badass than I normally feel, of course. Maybe you could transform into a primal or summon a primal god for this quest...or maybe one of the twelve

-Set up defenses and ensure enemies can't get to your base. You could set up friendly NPCs, build cannons, set traps, and maybe some Chocobo along a path. They stay wherever you put them and attack enemies as they come. Tower defense!