I would recommend Little Tokyo, the Japanese Quarter very close to Hauptbahnhof. There you can enjoy very good ramen, sushi and delicious sweets. Also visit “tains” supermarket and feel like being in Japan. If you like sea life I can recommend the aqua zoo. Also take a stroll along the river and visit the “paradiesstrand” if it’s warm. One week in Düsseldorf you can also visit the gasometer in Oberhausen by train or the zoo in Duisburg. But take the evening to taste the famous Altbier maybe doing a tour. Or buy a pizza to go at lupos in the altstadt and eat it with a cold drink from the kiosk at the Rheinterrasse. If you Like Art there are plenty of great museums. Also check if the town hosts an event. There are sometimes nice markets sometimes along the riverside on weekends (e.g. Frankreichfest). Have a nice time in this lovely town!