Mud Island, Memphis
I don't know about it being a "Must See" Activity, but it's been around for a while. It's probably better to go here if you have kids. I haven't actually visited the area since I was a kid other than to go to the concerts they have at the Mud Island Amphitheatre. I know there is a miniature replica of the Mississippi River from beginning to end. I remember as a child I liked to go there in sandals so I could take them off & walk through the river barefooted. I think there's also something about the history of the Mississippi River at Mud Island. Otherwise the only reason to go to Mud Island is to enjoy some great tunes at their summer concerts. It's a great place to have a concert because it's right on the river in downtown Memphis.
Small scale replica of the Missisippi river on an island downtown. Also, a visitors' center is on the same property
Mud Island is worth a visit. You can walk the skywalk, or you can ride the tram. They have a 5000 seat amphitheatre for concerts. They also have food and concessions, and a gift shop.