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Photo: Juloml, CC BY-SA 3.0 via Wikimedia Commons
Peaks like Veľký Rozsutec, or ravine Jánošíkove diery make this area very worth the day or two of stay.
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Pretty ravines and great overview from the top of the main mountain.
"Nízke Tatry" / Národný Park Nízke Tatry
Skiing, multi-day hiking and caves.
Many thousand years ago, this was one of the biggest Earth's strato-volcanoes, with diameter approx. 18 km. Nowadays though, it's completely forested and suitable for easy hiking.
This 13th-century castle of Gothic-Renaissance style is placed in a town of the same name. Nowadays, a museum of dolls and toys can be visited here.