It should be noted that the iconic hyperboloid nuclear cooling towers are actually unrelated to nuclear power. Many nuclear plants use them, but many do not, and many non-nuclear plants also use them.
The cooling towers are used to cool waste water before discharging back to rivers/lakes, if I am not mistaken. Too bad there's not a practical way to put that heat to better use.
Right. Nuclear plants turn heat into electricity the same way coal plants do, they just generate the heat differently, so the second stage of the process looks similar for both. Some plants are built where there's enough water flow (or enough lack of concern over the environmental problems) that the towers aren't needed.
For a while the Russians had a designed plant that produced electricity, steam heat for nearby homes, and desalinated water with what energy was left. Apparently the design was abandoned, which is kind of a shame.