I have not stayed at the Riverside state park campground but I did a drive by the last time I was in Spokane. The campground looked good. I would want a site by the river rather than one that is overlooked by the road into the park. The road into the park is kind of winding.
I also took a look at
www.spokanervresort.com this park looked fantastic but is a good drive out of town to Deer Park. They had great spaces ..You have to know that if I would consider a back up spot there that you would be fine.
Sean