It would help to know which part of the Outer Banks you'll be visiting and your ages. I don't know if you're in your teens or 20's or older so that would make a big difference too. But I'll try to give you a few suggestions.
You can travel the length of the Outer Banks and visit all of the lighthouses over the period of a couple of days. Riding the ferries is pretty neat too. If you approach the Outer Banks from the south you can get on a ferry at Cedar Island to Ocracoke. After you get to Ocracoke there will be a lighthouse very near the ferry terminal that you can visit. While in Ocracoke you can take her and browse around some of the shops and eat at one of their great restaurants.
The travel further north and visit Cape Hatteras. There is a beautiful lighthouse there that you can take her up in to the top. While in the area you can go to Buxton and walk around that town too. Or take along or rent a couple of bikes and ride around and see the town.
Then go on up further north to the Kill Devil Hills and Kitty Hawk area. There you can go to lots of restaurants and touristy shops and you'll pass another lighthouse on the way from Cape Hatteras you may want to stop at. While driving up be sure and stop along the way and walk out on the beach some with her. It's great and there likely won't be anyone else on the beach with you two.
In Kill Devil Hills visit Jockeys Ridge state park and check out the huge sand dunes and maybe take a hang gliding lesson. At least stay and watch the hang gliders some. Then go on up a few miles to the Wright Brother Memorial and see where they flew a plane for the first time. It's a great place.
There are great beaches and piers here too that you can walk on and do a little surf fishing if possible.
Then take the time to go all the way up north where the pavement ends in Corolla and see the wild horses and of course another lighthouse. After that you can take her back south through Kill Devil Hills and over to Manteo and walk through that beautiful town. Check out the waterfront area there with it's shops and great restaurants too.
That's just the beginning but I think it will get you started. Hope this helps and that you have a great time!
Where are you staying? I stayed in rodanthe at a beach house and it was kinda boring. The whole time we just went to the beach (it was may so it was very cold) the closest grocery store was 30 minutes away so we had to take many long drives. What you can do is visit tourist spots like some of the islands. I went to the kitty hawk museum and watched a movie and played laser tag. So I guess all you really can do is relax most of the time
