As far as the format of your cover letter goes, I would start (after your info, their info, the dear so and so) with a statement about hoping they will consider you for such and such position at whatever hospital (something of that sort). You want to talk about how you heard about this position, why you want to work there, etc.
In the next paragraph I think it's a good idea to relate some of your strengths to your hospital or unit's core values (what they are looking for). This shows you have done your research, but also shows why you would be a good fit with the hospital/unit.
The third paragraph in mine stated other positive traits I possessed, my work history and how it related, that I pride myself on this or that, etc.
Your last sentence/paragraph needs to wrap everything up nicely. Ie: I believe my skills and experience match up with the kind of nurse you are looking for. Thank you for your consideration.
I hope that makes sense. I didn't want to just copy and paste my cover letter on here. Don't be afraid to toot your own horn a little bit. Remember your cover letter is NOT supposed to repeat your resume. It is meant to go into more detail or explore things your resume can't. Good luck!