Yeah, right now Kentucky is the place. I think there are also elk in PA and Michigan. Theoretically, with more rain and vegetation, you would think an Eastern Elk might have the potential to grow larger.
When Moose were re-entroduced to New Hampshire there were a few good sized bulls. I lived up there at the time and there were a fair number around- I saw 7 in one day. I thought that for the first 10 years only "meat" bulls should be shot- any trophy sized bull ought to be spared and maybe the genetics would be passed on and there would be a realy good quality moose. Obviously it wasn't done. I got the idea after reading about some Texas ranches that wanted the inferior deer culled and the trophies spared.
Fall is the best time to see elk in the Smokies but they are around all the time. Last Summer I saw a nice one right near the visitor center on the NC side. Turkeys all over the place. One day I saw 13 deer and 13 turkeys.