The Giant Mountains offer plenty of hiking trails through deep forests and along the ridges of high mountains. If you like big hikes, then it is definitely worth leaving the valley and heading to the top of one of the surrounding mountains, preferably to climb Sněžka itself.
On foot from Chatta: There is no reason to drive or move anywhere, you can start from Chatta on the green hiking trail, after about 1 km you will come across the Toadstool Farm (an ideal stop for a trip with children), then you can continue to Janské Lázně and Černá Hora or to its foothills, where there is a newly built Treetop Trail. On the other side, you can go through the valley to Rýchory.
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