i grew up in chapel hill--i was initially diagnosed at duke but when my doc there retired when i was 4 i moved over to UNC and have been there ever since for my care. Close to duke though are Chapel Hill, carrboro, burlington (it's farther from the beach though...), cary...those are the smaller cities/towns in the area that i can think of off the top of my head. the larger cities are durham (where duke is), raleigh, greensboro, and the others that people have mentioned. the chapel hill/carrboro school system is good. some durham schools are better than others. Orange county school (the county where chapel hill and carrboro are located) doesn't have great schools.
I can't comment much on the duke clinic since i haven't been there in years but UNC pediatric and adult cf centers are wonderful.