If you happen to be there, stop by. But I wouldn't make a trip out of going to see this statue (and I'm an Elvis fan). However, Beale St. is half a block down from the statue and it's a lively, fun spot, even if it is a bit touristy.
I've never seen Gone With The Wind, but I still found this mill to be a really great place to stop. Lots of photo options. I went the first of April so I'd imagine it would be even better when all the plants and trees are in bloom.
I would suggest going when there is life in the park - Spring or Summer. Even Fall would be good. The end of Winter (April 1st), however, wasn't great. If you've never been to Garden of the Gods in Colorado Springs, CO then this is probably a good place to go, otherwise it's just okay.