Silkeborg offers different museums - with art (Jorn), freshwater science (Aqua) and the historical museum (the tollundman).
https://visitaqua.dk/
https://www.museumjorn.dk/da/
https://www.museumsilkeborg.dk/
You can go for a swim in different lakes
The old, traditional public bath - Badeanstalten - is also worth a visit. https://badeanstalten.silkeborg.dk/
You can sail to Himmelbjerget on the old steamer, Hjejlen, and enjoy the scenic view.
http://himmelbjerget.dk/
Or spend a day at the Bunkermusem with an interesting stories from the second world war.
https://www.silkeborgbunkermuseum.dk/