I grew up in Raleigh. Started at a run of the mill public school, then went into the gifted and talented program in the public schools, then went to private school in Cary. I've heard pretty good things about Chapel Hill. By reputation, Raleigh probably has the public schools unless you count the school of science & math in Durham. Cary is on the up and up but as a city it's just about the most boring picture of suburbia you can possibly imagine.
One thing I'll say about the gifted and talented public school programs in Raleigh-- although hopefully this is becoming less severe over time but probably not--is that it's basically a weird fucking race and class war. The public schools in the wealthy neighborhoods are not actually very good. The G&T programs are embedded inside predominately black public schools in what's more or less still the hood (was very much so when I was a kid). The bus picks you up in your expensive neighborhood, stops several times in progressively poorer neighborhoods, and then lets out at school in the hood where you have these white islands of G&T classrooms inside black schools. The tension (and occasionally violence) is REAL. But the schooling is good if you're lucky enough to make it into those programs.
One thing I'll say about the gifted and talented public school programs in Raleigh-- although hopefully this is becoming less severe over time but probably not--is that it's basically a weird fucking race and class war. The public schools in the wealthy neighborhoods are not actually very good. The G&T programs are embedded inside predominately black public schools in what's more or less still the hood (was very much so when I was a kid). The bus picks you up in your expensive neighborhood, stops several times in progressively poorer neighborhoods, and then lets out at school in the hood where you have these white islands of G&T classrooms inside black schools. The tension (and occasionally violence) is REAL. But the schooling is good if you're lucky enough to make it into those programs.