There is a short bridge to a small entrance on the west side of Orgrimmar that goes over the Southfury River. There is a very small spot below the bridge that can be fished and counts for Orgrimmar. It is hard to get to the exact spot and may flag you PvP trying to find the spot, but few Horde players look down there.
For Horde, one way to do this in Stormwind without dying is to go to the right side of the entrance on the other side of the mountains blocking anyone from getting in by foot. Mind you this requires the ability to fly. Go to the right of the small stone building, cast your line and successfully hook a fish and then you gain the achievement, assuming you have gone to Orgrimmar already.