As someone from central Illinois who has gone to the Outer Banks and Myrtle Beach, I can think of nothing better than to sit on the deck and sew while watching the grandkids play in the sand and water. Unfortunately when I went it was with a bunch of non-sewing friends so not only was there no room for my machine, they wouldn't even let me stop at a fabric store. We were pretty packed so there wouldn't have been room for fabric anyway but still........
You can't stay on the beach all day long and there's only so much sightseeing you can do. TAKE YOUR SEWING!!!! If anyone says anything just remind them that you are on vacation so you should be able to do what you want.