According to Randall Munroe, you'd actually experience less radiation about a metre under the water in a spent fuel pool then you do walking down the street.

https://what-if.xkcd.com/29/

On a tangent, I kinda love the fact that I've learned more about nuclear physics, orbital mechanics, and relativistic speeds from a poorly drawn webcomic than I have from any other source. (Ok KSP might actually have xkcd beat on orbital mechanics)