NWM pays below-market rates because they insist that it's an honor to work there. Others have addressed Stroger.
However...with experience, you should be able to get a job most anywhere else. Check out the Advocate system (IL Masonic is on the North Side), Rush, the Presence system, University of Chicago (which just came on-line as a Trauma center this year), Mt. Sinai/Holy Cross, the hospitals leaving Tenet, or the slew of independents (Swedish Covenant, Norwegian American, Loretto, Thorek, Community First, etc.).