The Giant Dragonfly, Tuna Kahuna, and Elite Ore are supposed to be the best 3 for medal farming.
I need to do more island runs with Club Tortimer for extra items.
I personally like Elite Scavenger whenever it's available. It usually takes about 3 minutes for 16 medals, but sometimes it can be done faster if you get lucky with finding the items. The quickest I've done it was about 75 seconds when all of my items were in the first three houses I checked and the houses were close to Tortimer.
If Elite Scavenger isn't there, then I look for Elite Ore Finder or Tuna Kahuna. I did Giant Dragonfly earlier and could barely find any dragonflies at all (plus, I was pretty bad at catching them when I saw them), but good thing the person I played with managed to get a lot.