It may be a bit far from Raleigh for you, but there are a few islands off the coast of South Carolina, Georgia and Florida which have beautiful beaches and lots of nature to explore by bike, kayak, boat tour, and more. The island furthest north is Kiawah Island - a luxury resort island where you can stay at a 5 diamond hotel, or rent a condo or villa for your stay. Kiawah is a peaceful and beautiful island about 40 minutes outside of Charleston, South Carolina. Charleston itself is a vacation destination with lots of history, beautiful architecture, world-class restaurants, and plenty to do and see. My online travel guide, http://www.sea-islands-vacation.com/ describes Kiawah Island (http://www.sea-islands-vacation.com/kiawah-island-sc.html) and offers personal recommendations, information, and tips on hotels, restaurants, activities, local events and more. You can also read there about other nearby islands, such as Hilton Head Island, and nearby cities like Charleston, South Carolina and Savannah, Georgia, which is a bit further south.
As for the Southwest, I'm afraid that's not my area of expertise, but I have vacationed in Sedona, Arizona and it was extraordinary. The red rocks are worth seeing!
Good luck planning and have a great trip!