Almost any beach in North Carolina will fit the bill - there isn't a lot of hugely touristy areas, just nice stretches of coastline!
We'll be at Sunset Beach in a week and I'm looking forward to it! I've heard Holden Beach and Oak Island are nice as well. We've been to Carolina Beach and Kure beach and they're nice, relaxing beaches - I like Kure because of the Aquarium, and while it's close enough to Carolina Beach to find restaurants, etc. it's not right in the middle of town.
We've also been to Emerald Isle/Atlantic Beach and those are nice beaches as well.
There are *tons* of rental houses and condos along the NC shore, and plenty of hotels, so I'm sure you can find something even now for later in the month. I don't know how cheap it would be, though. We've had some good results in general (not specifically in NC) using vrbo.com, which is vacation rentals directly from the owners.