Established in 2010, this national park encompasses a large wetland area and a number of islands in southwest Jutland near the border with Germany. With a high number of endemic species and migratory birds, this region is an important ecosystem worth exploring from nearby cultural centers like Ribe and Esbjerg. Yeah, this is hardly challenging your boundaries (unless you've got a Hitchcockian aversion to birds), but it is a unique corner of Denmark not often enough explored.
The Wadden Sea Centre puts together treks through the wetlands to catch oysters and interact with seals, while the mennesket-ved-havet ("men at sea") sculptures, unmistakable 30-foot high statues of four seated men peering out toward the island of Fano, are also a great photo opportunity in the area. For more information on what you can do at the Wadden Sea National Park, visit the included website.