in north seattle- dog friendly housing?

I am haveing a hard time finding afordable big dog (Rottie) friendly housing in the North Seattle area. Almost everywhere I look it says no Rots, and if it does accept them, it wants a big deposit and/or monthly pet rent.

Are there any places out there that do not charge an arm and a leg and will take me with my dog? When I say any, I mean even a MIL, studio, basment apartments, room for rent.....

My dog is older (not alot of energy, mostly sleeps all day), and EXTREMLY WELL TRAINED AND SOCALIZED (I am a dog trainer). She is friendly with other animals, people, and kids. Does not bark, soil in the house, dig, drool, jump, or chew. She mostly sleeps and hangs out at my feet.She is up to date on all shots, microchiped, and licensed. Plus, I have a pet resume for her, complete with letters of reference.

Any suggestions?