Talk to these folks:
WCAS Welcome
You are already covering a lot of territory in your questions. The schools here are by county, so the Wake County school system is very very large. "Supportive" in the context of special services varies a lot by school. Duke is not in Wake County; it is in Durham County and you may want to look there too. TEACCH is a statewide program and the local centers are in Raleigh and Chapel Hill. I've heard they have long lead times, though, and I know a lot of folks with kids with autism who haven't used TEACCH much. If private school is an option for you then you may want to look at the Mariposa School
The Mariposa School for Children with Autism . It gets great reviews.
Once you've narrowed down where you want to be for schools then folks can give you better suggestions on where to live.