Well that is the Triad which puts you about 2 hours and change from the mountains. Definitely check out Grandfather mountain and that area. Lake Norman is cool for sure as well. I am in Raleigh about an hour east of Greensboro which can be a fun place to visit. You will be about 3-4 hours away from the closest beaches (which are actually at the end of I-40). I would avoid Myrtle Beach in SC though. If you can invest the extra time (5 hours or so) drive to the Outer Banks. Finally in NC, Fayetteville and much of the coastal plain region (inland) is kind of the armpit region of the state.