Seattle Hospitals

You could actually find out a lot of this through the labor contracts, start with SEIU1199nw, and WSNA, those are the two big ones that cover most of the hospitals:

Chapters | SEIU Healthcare 1199NW

Union - Washington State Nurses Association

As for a place to live, I'd steer clear of southern suburbs and parts of peirce county. You can use Neighborhoodscout to get an idea about crime rate and public school quality:

Washington Real Estate Information - NeighborhoodScout

I personally grew up around Kitsap County- Bremerton and Port Orchard. If you work in Tacoma, it's a 30 minute commute, or you can take the Fauntleroy ferry to south Seattle- ~40-45 minutes to cross. In Northern Kitsap county, you can use the Edmonds ferry to cross to northern Seattle, about the same commute time.

I could also recommend living on the east side, though it's a bit more expensive. Issaquah, Bellevue, Kirkland, and all the areas surrounding it to the north. 30 minute commute time in average traffic times to Seattle, probably a good hour to commute to Tacoma though. Just my two cents. I don't know a whole lot about this area, Someone that's from the eastern side could probably tell you more.

There are some very nice cities in the south sound. Puyallup, orting, Sumner to name a few.

Snoqualmie is very nice and close to Issaquah Swedish. However that area is very expensive.