Nothing super close other than Mt Spokane. Check out the Tour section, there's also Lookout Pass on the North side of the road, which the loc's call The Training Grounds, No real avy concern and simple up track for turns back down to the road.
When the snow level get's really low (down to town with 12+inches).. you'll see some postings about some special spots... (see my post "Who's ready for winter" for a clue there.
Welcome to the area!
Cheers,
PP