Although not strictly on an Outer Banks island (it's part of the mainland), this 154,000-acre wildlife reserve of wild lands and waters is managed by Dare County. It's home to black bears, river otters, wild turkeys, deer, bobcats and eagles. If you're hoping to see an alligator, you're out of luck. The name comes from the shape of the park, not because the reptiles live here.
Most of the park consists of self-drive safari, but there are a couple of short half-mile walking trails too, plus paddle trails for boaters. The visitor center is located in Manteo and has an exhibition on the wildlife found in the park.