The Zittau Narrow-Gauge Railway runs steam trains from Zittau into the Zittau Mountains, with branches toward Oybin and Jonsdorf. It is part transport, part excursion, and a good way to make the surrounding countryside feel close rather than abstract.
The ride is especially useful if you are visiting without a car. You can see Zittau's old centre, then spend the rest of the day among sandstone hills and Upper Lusatian villages.