I can give you the general impression by many people of schools in the local districts, though you should also check the school websites.
The best are Chapel Hill Carrboro schools
Next are the Orange schools
As a generalization, Alamance, Chatham and Durham schools aren't that great, though it depends on the particular school and the teacher.
Northern Chatham, the area closer to Chapel Hill has oood schools, one of them is a charter school, supposed to be quite good.
School taxes are very high in Chapel Hill/Carrboro. Lower in the other areas.
A lot depends on what your child needs. My daughter went to a charter school that fell apart, then she went to Carolina Friends School in Durham. It was the right school for her, wrong school for my son. You have to know what your child needs, the right atmosphere, and consider whether s/he has any learning disabilities.
Don't know if this has been helpful or not. Feel free to contact me for more specific info.