Nuclear power plants are thermal power plants and that means they need cooling. The power density of nuclear power plants is so high that most of them can't be placed near rivers because rivers have a variable flow rate.
If the flow rate is too low you risk killing aquatic life in the river ecosystem so instead the nuclear plant is turned off. You can avoid this by placing the nuclear power plant near the ocean. That's what the Japanese did with the Fukushima power plant even though it's a tsunami prone area.
What gives you the idea that nuclear power plants can't be placed near rivers? Almost all that aren't on the coast are near rivers.
And they don't need to use potable water. The Palo Verde plant uses wastewater.
Because humans need water to survive, all population centers are built with access to water. Thus, cooling is available pretty much anywhere one would want to build a nuclear plant.
If the flow rate is too low you risk killing aquatic life in the river ecosystem so instead the nuclear plant is turned off. You can avoid this by placing the nuclear power plant near the ocean. That's what the Japanese did with the Fukushima power plant even though it's a tsunami prone area.