Do you wish to roam farther and farther?
See the good that lies so near. (Goethe)
The Brocken summit: Today site of a radio and television transmitter and a weather Station
A weekend in the mountain range of Harz in August: Sunny and warm. Perfect to follow the Goethe path up to Brocken, the highest peak (1.141 m) in Northern Germany and part of the Harz national park. It will take you a half day for the 16 km hike path starting from Torfhaus, leading to Brocken and returning back to Torfhaus.
There are also lots of other hiking trails, natural sites and historical towns to visit.