There are variety of fun and historic attractions to explore in North Carolina like Cape Hatteras National Seashore and Lighthouse, Charlotte Motor Speedway, Grandfather Mountain, Great Smoky Mountains National Park.

Those are all a long way from the Triangle, alex_carter!

High school seniors or college seniors or Old Goat (my category) seniors?

Check the university calendars (NC State, Duke, Carolina) online to see what is happening in the way of cultural events. Pray it is not graduation weekend for any of them.

The one thing I could absolutely recommend to any of the categories of seniors above is lunch at Allen and Son BBQ just north of Chapel Hill. It hasn't changed since I was in grad school in the 1970's. You can then continue north to the charming and historic town of Hillsborough to work off your lunch with a nice walk.

The art museum (Ackland) at UNC is interesting, and both Chapel Hill and adjacent Carrboro have interesting shops.

The art museum in Raleigh is very good also. There is a planetarium at UNC. Lots of good food in Chapel Hill, including Crook's Corner where shrimp and grits was made gourmet fare. A Southern Season in CH is a cooking store on steroids. They have a nice lunch also. The Raleigh Farmer's Market is interesting/fun. The Vietri pottery outlet is in hillsborough.
You might look on Hotels.com for a hotel.

Durham:
Duke Chapel
Sarah P. Duke Gardens
Nasher Art Museum
Museum of Life and Science
Duke Homestead

Chapel Hill:
UNC Campus
Franklin Street
Ackland Art Museum
NC Botanical Gardens

Raleigh:
NC Art Museum
NC Museum of Natural Science
NC Museum of History
Historic Oakwood area and cemetery
Moore Square
Mordecai Historic Park
State Capitol
NC State Arboretum

"Best" place to stay would be Fearrington House or Umstead but in the Embassy Suites price range you've plenty of choice and with a car it doesn't much matter where in the Triangle you stay. Plenty of good places to eat in all three towns. NY Times just did a piece on Durham:

http://travel.nytimes.com/2013/01/20/travel/36-hours-in-durham-nc.html?pagewanted=all&_r=0

Also check the event calendars here:
http://www.progressenergycenter.com/
http://www.dpacnc.com/
http://www.playmakersrep.org/
http://www.raleighlittletheatre.org/
http://www.artscenterlive.org/

How could I have forgotten Crook's Corner. My goodness, it is the place where I knew that my son's girlfriend was the right kind of girl when she stole fried oysters off my plate. She is now the mother of my granddaughters, and I would still not trust her around my oysters. Yes, it is a must.

Yup, that's how you get good blood back in the family!! LOL

I dream about Crooks Corner's hoppin' john. And have y'all tried their homemade tonic water in a gin and tonic? It's the perfect drink on a hot Carolina night.

-definitely park near the state capital and check out the grounds. it's my favorite place to bring out of town visitors. several monuments and statues to check out.

-Christ Church is within easy walking distance. (It's a beautiful little Episcopal chapel to sit even if you're not religious. Not always open though)

-Lake Johnson in South Raleigh is IMO Raleigh's prettiest lake and has lots of walking trails through the woods. There's a boathouse where you can take a paddleboat, rowboat, or motorboat out.

-and please do visit the Pit for an authentic North Carolian BBQ experience.