It’s not easy to find a “home stay” for 1 or 2 weeks, I saw a lot of houses for “Home Stay” in Vancouver and Toronto for 1 or 2 weeks, but it’s not in Seattle.
The concepts of “Home Stay” in this area is for several months.
If you would like to find from Korean, you can check in
http://www.kyocharousa.com/

You can stay in Hotel or Motel, but those room rates are $70- $150, I saw some extended stay Hotel or Motel, but one of Extended Stay Hotel which is located near by my office(Bellevue) is full for whole next month already.
And if you are looking for a Apt or school zone, let me know.
I moved in Seattle area last year.

Doug

>이달말에 가족(4인)이 시애틀로 갑니다. 집을 구할 동안 1,2주 정도 머물 저렴한 하숙같은 곳이 있는지 궁금합니다
>
>모텔도 가격이 적당하고 안전하다면 괜찮을 것 같기도 합니다. 시애틀에 계시는 분들의 정보를 기다리겠습니다

“Extended Stay America” Hotel is good for staying weekly basis. Each room has small kitchen area as well. I have stayed the hotel near Tacoma, and the rate was about $340/week 3 yrs ago.