I would encourage you to get out of the city and visit the surrounding countryside. North Carolina is a beautiful state, with lots of history, including a lot of Native American history which you may find particularly interesting.
The people of North Carolina are particularly friendly, and the atmosphere is generally casual and open. You will find that most people greet you, strike up conversation, and will be curious about your nationality, accent, etc. They have delightful southern accents themselves!
Southern food - Mmmmm, mmmmm, mmm! Southern desserts are especially good - all sorts of pies and cookies. Yum. Lots of vegetables, cooked all sorts of ways, and I hate to say it, but lots of fried food as well. Check out chicken and dumplings if you get a chance!
I think you're in for a treat. If you can, check out the Shenandoah mountains (absolutely beautiful) and/or the Atlantic beaches. North Carolina has some beautiful Outer Shore beaches where herds of wild horses roam.
Good luck - you're going to be visiting a beautiful state! And I wouldn't let the "very religious" aspect put you off. It's not like you're going to be beat over the head with Jesus. They are just more regular church goers than you are probably used to.