>>1045395Hey, OP, North Carolinian here. I think your idea to visit the Outer Banks and Washington is pretty solid.
I've somehow never been to the NC coast, but I've heard good things. I have, however, been to Washington, and, as anons have said, it's pretty nice and has lots to check out.
The drive to both of those places isn't too bad (at least, to my American standards). If you're in Washington around April 6-8, you might be able to catch the famous cherry blossoms.
Also, NC itself is a pretty alright state. Chapel Hill isn't terribly exciting, but it's got some good restaurants, and Cat's Cradle in nearby Carrboro attracts some pretty good music. I recommend trying some NC barbecue while you're around. Also, if you feel homesick, check out a sort-of-german-themed restaurant/bakery in the Chapel Hill area called Guglhupf.
I'm not sure if you're going to do any travelling during your month in North Carolina, but if you do, I recommend the Blue Ridge Mountains in the west of the state, which are part of the Appalachians. The region is beautiful, and the culture out there is, if nothing else, uniquely American. There's also a 90k population city out there called Asheville that is pretty awesome (I went to college there) and has really good food, beer, and hiking opportunities. I think Asheville is a little over 4 hours both ways from Chapel Hill. Just something to consider.
Hope you have a good visit.