For a relatively small city, Omaha has excellent health care. Two hospitals share trauma duties, the NE Med. Center and Creighton (which the locals sometimes refer to as St. Joe's Hospital.) http://omahatraumasystem.com/
The economy here, while much better than most areas of the country, is slower than normal, which has affected health care somewhat. There are a number of nursing programs in the area, so new grads are plentiful. Most seem to find jobs, although not always full time and not always the area of their choice.
As an experienced nurse, I don't think you would have too much trouble finding employment. These are the major systems in the area. You can Google their websites:
The Nebraska Medical Center/System
Creighton University/Boys' Town
Children's Hospital & Med. Ctr. of Omaha
Methodist Health System
Alegent Health System
Nebraska Orthopedic Hospital
Omaha is a nice city with plenty to do and offers a good quality of life. I could live without the winters (although this one has been quite mild).
Hope you can join us