Narrowing it down to one is tough....I would have to say trout fishing in New Zealand. The island which is less inhabited...where the hobbits went
I know, it is trout and we can get that here but something about the particular beautiful setting and it is supposedly the best in the trout fishing in the world.
I think tarpon or goliath grouper would be close 2nds.
Good on you for chasing the AB species! I don't think you will have much trouble with grayling or bull trout. Both pretty willing to take flies...bulls...pretty much anything on a good day.
Good luck and good fishing!