Greensboro, Greensboro, Greensboro!
Fisher Park neighborhood, close to downtown; Aycock neighborhood, also near downtown; College Hill district, near UNC-Greensboro & Greensboro College, right smack in the middle of downtown (well, a little south of the middle of downtown).
http://www.fisherparknc.org will give you a primer on all these neighborhoods, as I recall.
Real estate: One of the oldest firms in Greensboro. Owners are from Greensboro and know the area -
www.yostandlittle.com - Search within the 27403 zip code, which is downtown and environs.
Best of luck and hope you find what you're looking for in The Gate City!