Apart from Salwa Road, there are a few Car Wash Centres in Matar Area as well. While going past the Airport Signals on Airport Road towards Wakrah, take right on the next signal & you'll see a few on both sides of the road. Atleast a couple of Centres are there on the B-Ring Road, opposite side of Um Ghuwailina Area in between the Auto Decoration Shops. A few Car Wash Centres are on Bin Dirham Street in Mansoura Area near Qutba Restaurant.
Hope it helps. :-)