And you might wish to check on www.bahn.de. There are quite a few choices that can be done within three to four hours of travelling. However, if you want to see something and do not want to spend half a day on the train, I would concentrate on 120 minutes of travel time at the utmost (this would bring you as far as Frankfurt or Amsterdam). Other destinations within reach are certainly Cologne and Bonn (20 or 40 minutes, Aachen (another 20 or so minutes from Cologne). You could eg do one full day to Cologne, Bonn and Aachen (I would chose two of the three) and a further day in Amsterdam.

Travelling to Sinsheim or to Luxembourg (close to four hours by train) from Düsseldorf sounds very American but more than exotic for a local. The city and its surroundings (cities like Duisburg, Oberhausen, Essen, Gelsenkirchen, Dortmund, Mülheim) are all quite big cities for German standards, are in reach withing 10 to 30 minutes by train and have plenty to offer; I would not waste my time by doing all that travel.