Thank you for your email. Two nights on the Outer Banks during August will require a hotel stay, because the rental companies only rent out by the week at that time of year. You may, however, give a few of them a call, as you might find a house that has not rented and will give you a good price.
All that being said, here is a listing of Outer Banks hotels. If they are hyperlinked, you will also be able to get information, pictures and rates on the hotel for the dates you desire. I believe they will allow you to sort by rate so you can find the cheapest.
One other thought is you might consider an Bed & Breakfast as an option. Here it will not be as impersonal as hotel, and your breakfast is provided.
Hope this helps and enjoy your time on the Outer Banks!