Hey OP, this website might help you a bit (assuming you're already in Denmark). Unfortunately it's in Danish, so if you can't read Danish, I guess Google Translate is your friend. It's a interactive map sort of thing, where you can choose what kind of experience you're interested in, in DK - hiking trails, campsites, shelters etc.
http://www.udinaturen.dk/And to all the haterz saying we aint got shit - you're right. But we make the best of what we've got. At least we have some semi-decent forests and a hell of a lot of coastline. DENMARK STRONG