Bad Harzburg is a pretty thermal spa town which provides you the few hiking trails to explore Germany.
You can start hiking to Grosser Burgberg. It is a hill above Bad Harzburg, which has the ruins of an 11th century fortess which was built by Heinrich IV. Just continue the trail by Bummelalle to the Kurpark. Just follow the marked hiking trails which will leads you to the national park from Berliner Platz and Grosser Burgberg.
You can also do the Hiking to Berliner Platz to Sennhutte, Molkenhaus, Rabenklippe and the Ecker Valley. From Grosser Burgberg you can also take the Kaiserweg trail which will take you to Kaiserweg trail and then to Torfhaus and then finally to the Brocken. You can also have a view of Radau Waterfall which is 7km from Grosser Burgberg.
If you are lucky enough with the weather than you can also ski cross-country to and from Torfhaus.