This is what lots of people from my area sound like. Predictably kind of a hybrid of North Carolina & West Virginia.. a southern drawl with a little bit less twang than what you'd ordinarily hear in deep southern states like Mississippi or Alabama. Some local people have it much thicker, others very little:
[youtube]http://www.youtube.com/watch?v=K2I0d1DHZas[/youtube]
I grew up in southwest Virginia, but since my parents weren't native to this area & don't have the accent, I personally don't speak with one most of the time either. Every now & then it can creep into my speech, though, especially if I'm talking with other people whose accent is more pronounced than mine. It also comes out in the way I say a handful of words (I pronounce "syrup" more like "sirrup," for instance) but usually, the only way that people can tell that I'm from the south is when I use a word like "y'all" or "soda" (rather than pop), which are both things that I say fairly often.
Also, even though I don't speak with a southern accent, I think it can be really attractive when a girl has a nice refined one. I think it's the most pleasant-sounding American dialect when the speaker doesn't slur their words & sound like a hillbilly.