Pond to raise Fish in - Plump up those fishies, amphibians, coral etc
Mog net mail delivery - Delivering moogle mail and getting to hear what the moogles have to say to one another.
Chocograph treasure hunting - Bassically your given a picture and have to find where it was shot to dig up the treasure with your Chocobo.
Quiz npc/monster - You have to answer trivia questions relating to the game lore and possibly the area.

Thats all i can think of right now but i might come back with some more later.