Walking from the Untermarkt down to the Neisse River takes you to the Old Town Bridge (Altstadtbrücke), which connects Görlitz to its Polish twin city Zgorzelec. Since Polish accession to the Schengen Area in 2007, crossing the bridge requires no passport or checkpoint — you simply walk from Germany into Poland in a matter of seconds, which never quite loses its novelty.
Zgorzelec has its own character — slightly more workaday than Görlitz, with good Polish restaurants and cafes and the interesting Landscapes Museum documenting the shared history of the two cities. The walk along the Neisse itself is pleasant, with good views back to the Görlitz Old Town from the eastern bank. The combination of two countries separated by a narrow river, with completely free movement between them, is one of the most vivid expressions of what the European project was supposed to achieve.