I known the place. It was known as Providence Hospital before Swedish took it over.
If you are willing to commute, there are certainly a lot of choices. Even nearby the hosp, there will be lots of choices but it will be much more expensive. It's expensive to live in Seattle so there is a trade off.
If you wont be working the 8-5 M-F shift, living outside of the downtown area and commuting might be worthwhile.
If that is interesting, send me a pm or call or text.