Well that's crazy. The Hilton site said that Mainz was only 19 miles from the center of Dusseldorf. It is a good thing that I asked here.
I will go back and check for Cologne, or maybe even become adventerous and try a non-Hilton hotel.
You are so right,
soitgoes, our show passes do include local rail fares. I will check out Essen. We actually have friends who live there so it would be a good chance to see them as well.