You can stay a block behind the Coulee Dam Casino.
http://www.colvillecasinos.com/casinos/coulee-dam-casino/
"Click for directions" at the bottom of the website. Zoom into the Google map and you can see the two nearly empty parking lots beginning at 6th St. and Fir St. have about six lined spaces for RVs (parallel to 6th St). You must go get an overnight parking permit from the casino. Can't remember how many nights they allow. You might want to call them to confirm. I stayed there last year and a few years before that.
This is really close to the dam and free!