Thanks, everyone, for such helpful responses. The first few all voted for Cologne, so I thought, "Well, that's an easy decision, then!" But then I saw the responses in favor of Dusseldorf. Darn you all for being so knowledgeable!

If I decide to go to Cologne, would you recommend the Four Points Sheraton? I found a rate of 97 Euros per night, including taxes and breakfast.