The center of Klettenberg is home to cultural attractions like DDR-Museum, so you might want to stop by during your stay. If you want to experience more of the culture Klettenberg has to offer, head to Walkenried Abbey and Bad Sachsa Fairy Tale Ground.
Dom Zum Heiligen Kreuz is just one of the places to see in Nordhausen, so why not enjoy the other things to explore during your travels? While you're in the area, wander around the forests.
You can get tickets for a performance at Theater Nordhausen/Loh-Orchester Sondershausen on your trip to Nordhausen. Take in the museums while you're in the area.