Nucs have to be near a water source.
There are actually several rivers which could be used for that purpose in each of the states mentioned
No, actually they don't. It's just a lot cheaper to build a once-through water heat exchanger than it is to build a closed-loop air heat exchanger.
The Palo Verde Nuclear Generating Station where I work is 40 miles west of Phoenix with no lakes or rivers nearby (the Hassayampa River is within 5 miles, but it's dry). The cooling water for the plant comes from the 91st Avenue water treatment plant in Phoenix. It's piped about 35 miles to the plant, cleaned up, and supplied to the evaporative cooling towers. I think it's the only nuclear plant in the country that's not adjacent to a lake, a river, or the ocean.