Two places come to mind immediately in the Tri-Village (Rodanthe, Waves and Salvo). The first is the Reef located in Rodanthe on the Sound side. The Reef looks like a t-short place from the outside, but has all sorts of beach stuff when you go in. As you go in, walk to the back left hand side. I believe you will find chairs there.
Down in Waves, you can try the hardware store called Dare Building Supplies. It is on the Ocean Side of Rt 12. They also have all sorts of beach stuff in the front of the store.
Hey, if you have time, we'd love for you to add a picture from your vacation ... using the beach chairs!