I have a ford explorer, so it chugs gas.. but it'll do.
Although, I did stay in the back of a explorer while tucked in between some dunes on the north side of oregon inlet many years ago. I wouldn't try it now though. There is a huge beach access fight going on in OBX right now and even the those in favor of 4x4 beach access will probably rat you out so you don't spoil it for everyone.
You could also pretend to fish all night and get a few zzzz's. The beaches are open 24hrs until april 30.
Check out the faq at the top of this page:
Haven't been in a while, but a few campgrounds around lighthouse include: Cape Point, Cape Woods, and Frisco Woods. Not sure if they're still open.
Frisco Woods and the Frisco National Seashore campsite should be open in addition to the NPS site next to Oregon Inlet -- check the NPS site link (above). You can also rent motel rooms rather inexpensively this time of year. Check the surf forecasts when you leave before committing to a specific place to stay... many miles and hours between Nags Head and Frisco, but certainly is more beautiful south of the Bonner Bridge.