As a couple, Potsdam & Sanssouci Palace (day-trip) works.
Sanssouci's terraced vines, fountains and the wider park of palaces make a properly grand day out, and Potsdam's Dutch Quarter and Cecilienhof add depth. The catch: the park is enormous and footsore, Sanssouci itself enforces timed tickets that sell out, and doing it justice eats a full day.