+1 for Dusseldorf .. It's not far at all .. If you're going to the Messe for an exhibition or similar in Cologne then there's often trains from DUS Airport station to Koeln Messe/Deutz which is right at the Exhibition Centre.
As an aside - In theory you're supposed to have a ticket to ride on the funny cable car thing from the Airport Terminal in DUS to the nearby mainline Train Station .. but I've never really managed to get the vending machines to work and I suspect nobody really does buy a ticket