Hi Juststudying,
You should have tremendous choice in your price range. I would highly recommend checking out Chapel Hill & Carrboro; their school system is the highest ranked in the state. Very rigorous curriculum, highly involved parents, excellent gifted and special ed programs. You can get more info and compare all of the school systems on
GreatSchools.net and
ReDir.
Chapel Hill and Carrboro also offer a lot of diversity, as do the Durham neighborhoods that everyone has mentioned. Tons of families with young children wherever you go. Some neighborhoods to check out in Chapel Hill would be Lake Hogan Farms, Creekwood, Meadowmont, Southern Village, The Oaks. Many of these communities have swim and tennis clubs, walking trails, playgrounds. Southern Village and Meadowmont also feature elementary schools within their communities, as well as village centers. Great walkability!
I moved here from Boston 17 years ago, and it's a very easy transition. There is as much culture and arts here, in my opinion, for this size community. We have wonderful symphony, broadway shows, art walks, performing art centers, regional theatre -- anything you could ask for. I did not feel I was losing anything culturally making the transition from the Northeast.
Best wishes.