I'm not a nurse (was a lab technologist for years, some years ago). The place I lived before where I do now had an apartment building across the street that housed nurses who temped for six months at a time, if I remember correctly. For them it was a good way to both travel and earn money. So, I'm guessing that such nurses, at least in the U.S., do cover some local jobs. But... our small city, being somewhat out of the way, had trouble getting medical professionals to move to it in the first place, so this is a two way street.
I've no advice except to try to find what you can in the way of nursing websites in your new state, including nursing blogs that might be relatively local.