I toured in Denmark in June many years ago. I rode in a big counter-clockwise circle, crossing the border from Germany, and arriving back in Germany on the west coast island of Sylt by ferry from a neighboring Danish island. The delightful little island of Aero in the Baltic is not to be missed. Funen, a much larger and more densely populated island was also very enjoyable. Funen had pleasant gently rolling hills, not dead flat like the area north of Copenhagen. One part of southern Jutland had some actual hills, but nothing too serious. Despite riding in a large circle, I managed to have headwinds every day. Really. But I was lucky insofar as the rain was concerned. Though it rained often, it rained almost exclusively at night while I was there. Mostly hostels (uniformly excellent) with some camping.