The Mississippi at Memphis is a genuinely impressive thing to see. The river here is around a kilometre wide, running fast and brown through a sweeping bend, with the flat Arkansas bluffs stretching away to the west. Tom Lee Park, the long riverfront green space that runs along Riverside Drive, gives you the best prolonged exposure to it — walking the length of the park with the river on one side and the Memphis skyline on the other takes about thirty minutes and costs nothing.
The river is the reason Memphis exists: it was the crossing point, the trading post, the distribution hub for everything moving down the Mississippi Valley. Standing on the bank, watching tow barges push their loads against the current, it is easy to see why. The Great River Crossing statue and the surrounding Memphis park system give you a civic version of this; for something more private, walk down to the rocks on the Mud Island side and sit with the water moving past. The river is higher in spring, following the snowmelt upriver; in summer and autumn it drops and sandbars appear.