The Eifel National Park is a region of beech forest in the North Rhine shouldered by man-made lakes and a man-made border with Belgium. Located an hour's ride southwest from Cologne, the park is most fully experienced through its aptly named "wilderness trail," which can be broken into four day-long stages that cross forest, plateaus, dams, and plenty of viewpoints to inspire the revelation that you're glad you aren't doing that sight-seeing tour in Berlin. The Eifelsteig is another lengthy walking trail (313 km) through the park that can be done in manageable stretches; take the fourth stage (Einruhr to Gemünd) to experience how Eifel can best be encapsulated in a day of hiking.
Perhaps most interesting about Eifel National Park is its connection with past wars. Certain areas are clearly cordoned off due to live mines still being in the ground, while Ordensburg Vogelsang, the infamous former Nazi estate and military training grounds for the "elite" race of humans is still preserved and is open year round to visitors. Entrance is free, while English-language group tours will run you under $10 USD and are well worth the insight, especially when combined with a hike from the nearby Urft Dam or any other stretch of nearby trails.