I am from Seattle, currently in St. Louis for school, and I have a suggestion for you. I think the dorms at the UW have summer stay options, although I don't know if they offer monthly stays. Call their housing office and see. Also, the University district area of Seattle, just North of the campus, is very cheap. It is also dirty and noisy at times, but you could probably find something there. The UW Daily newspaper should be online now, so you might want to look ther in the classified section. Good luck and I'll see you in Seattle- I'll be doing trauma that month too.