Don't know much about the Virginia side (though Ellis Maples' Chatmoss CC is up that way and is pretty good) and Danville CC is reported to be a good Ross course (haven't played it). I believe both are private.
Once in NC, two privates to consider are Deep Springs CC in Stoneville just across state line (very good Ellis Maples course) and Pennrose Park (9 hole Ross -- I have not played it) near Reidsville.
Sedgefield is great, and there are several other very good private courses in Greensboro (GCC has 2, the Cardinal by Dye, Forest Oaks by DLIII and Starmount Forest - Stiles & Van Kleek redone by Lester George). On the public side, Greensboro National and Bryan Park are good, and High Point's Oak Hollow is very good Dye (with Coore).
About 30 minutes south of Greensboro is Strantz' Tot Hill and 15 minutes beyond it is Old North State by Fazio.
To the West 30 minutes is Winston-Salem, with Old Town, Forsyth CC, and Tanglewood, among others.