J.C.
I don't think anyone will think twice if you put an address label.
I do think that your living out of town is your main concern for worry. I would address that first sentence in a cover letter.
I am moving to the XXX area on December 1, 2011 and would like to be considered for the RN position available in your office...
Also, blindly mailing resumes is often a waste of time. Go on Monster and see who is has available positions.