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Not in Great Fatra nor Liptov, but right at its edge. You can spend a few days here, esp. because there is plenty of hotels and non-ski activities (e.g. park for kids).
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Cyklokorytnička
A bike road in place of former "small train" track, mostly flat - it's a nice all-day long trip for families, as you can avoid the main road on most of it. Korytnica used to be a famous spa area, but now it is somewhat degraded. There are some restaurants and mineral water springs in the area.
The hike up is quite steep for an hour or two.
A relatively small aquapark with a pool, few whirpools, wellness, bowling and minigolf. Also pizza available.
A secluded and small one, only 400 m.
Brankovský vodopád
Highest waterfall of Low Tatras, especially nice in winter.