Great area, however coming from a TFI unit as your first tanker assignment, both of you aren't going to like the ops tempo. The club has closed, never had a golf course (however there's great golfing off base), newer BX and commissary, brand new gym, nice outdoor running track the three months Spokane has nice weather. Hospital was renovated while I was there.
I know they were building/renovating base housing when I left there in '10. If you want to live in Spokane, I'd recommend upper South Hill. A lot of people live over in Eagle Ridge off I-195. I wouldn't live in Airway Heights, though it has improved since I first got there in '06. Spokane Valley is too far of a drive IMHO. I would stick to the far northwest(Nine Mile Road) side or the south side (South Hill) personally. Gas prices are about as ridiculous as the north east, so the commute might factor in how far away you want to live away from the base.