One of your first stops should be National Park Center Saxon Switzerland. Here, you'll be able to find your bearings and get some great ideas before you start exploring.
This tourist information center won't cost you a dime, which is fantastic news if you're after free things to do. You'll find National Park Center Saxon Switzerland in Bad Schandau. There are plenty more attractions to visit not far away, including Koenigstein Fortress, Elbe Sandstone Mountains and Bastei.