All the towns in North Idaho get pretty much the same amount of sun. That's because most overcasts are from widespread regional weather systems that pack moisture up against the Bitterroots, and aren't local.
If you go to the Western Regional Climate Center, they have a page listing percent possible sunshine for a few stations
http://www.wrcc.dri.edu/htmlfiles/westcomp.sun.html
Spokane is representative of North Idaho, and you can compare that to Boise or wherever you wish. Nov-Dec-Jan are below 30%, those are the dark months, but they're regularly punctuated by bright, clear days, too.