Surprisingly, the O'Doughrety's in the Spokane Valley has GREAT BBQ, and the Globe downtown Spokane is decent. As far as a TRUE BBQ joint, have not found one in the area as of yet but those two produce decent BBQ.
The best BBQ in Spokane is Smokies BBQ located at 3415 E. Trent Ave. On the corner of Trent and Freya. Cute little joint. It is a drive thru but they do have outdoor seating in the summer. I am from Texas and this is the best I've had since I was back home.