I agree about the hospital in Fayetteville not being a great place...a couple of days there with my daughter and I demanded they transfer her to Duke!
Anyhow, if you were looking at the big hospitals, Duke in Durham and UNC Chapel Hil,l then maybe Fuquay-Varina would be a good starting point, just about in the middle, a somewhat longish commute at 40+ min each way, but I imagine that with nursing and working on base you work other than "typical" hours and can possibly avoid high traffic times which would ease things.
I remember driving thru the area on my way home to Fayetteville (I've since moved to Charlotte) from Duke one day (trying to avoid traffic on the highway) and it was a nice area!
Another thought, but I don't know how the hospital is, is to look at Pinehurst, there's a regional hospital there, here's a link:
Moore Regional Hospital
That would allow you to live in the Pinehurst/So. Pines/Aberdeen area, also nice.
Good luck.