Düsseldorf and Amsterdam are both wonderful cosmopolitan cities with so much to offer! When I have limited time in a destination, I like to combine a cultural institution of some sort, with plenty of strolling to get a feel for the city.
Get an early start on your first day in Düsseldorf and if you’re interested in modern art, the Kunstsammlung Nordrhein-Westfalen (Art Collection of North Rhine-Westphalia) is excellent. It has several different spaces—one with important 20th century artworks by artists including Picasso, Klee, and Richter; one with edgier artworks since about 1980; and the Schmela Haus, which is used for experimental art. After the museum, head over to the the Alstadt, or Old Town, for lunch. It’s a small area (1/2-square-mile) that’s jam-packed with cafes and restaurants.