Eupen is Belgium's German-speaking capital, tucked into the eastern edge of Wallonia near Aachen and the High Fens. It is not grand in the way Bruges or Ghent is grand, but it has a useful oddness: Prussian history, Belgian administration, a baroque market church, contemporary art, and forested hills all in one small town.
The upper town around Marktplatz and St. Nicholas Church is the natural starting point. From there you can walk to the city museum, IKOB, and the little viewpoints over the lower town. The architecture is a reminder that Eupen changed hands more than once, and the street life feels closer to the German border than to the Meuse valley.
The better reason to stay a day is the landscape just outside town. South and east of Eupen, the Hertogenwald and the High Fens begin to take over, with darker woods, reservoirs, and boggy uplands that feel far from Belgium's busy lowland cities. Lake Eupen and the Vesdre Dam make the easiest nature excursion if you do not have time for a longer hike.