From a tourist perspective, I think the Rhineland, i.e. Rhineland-Pfalz as appealing or more so, than North Rhine-Westphalia to which Caspritz78 refers.

Picking up on Etch5895's suggestion, a nice Rhine cruise on the KD Line from Bingen to St. Goar or Boppard is a lovely way to spend a day - you can get lunch on the boat or, for better food and more options, in St. Goar or Boppard.

A slightly less appealing, but perhaps more cost effective approach would be to drive up the Rhine Gorge.

If you are interested in Cathedral cities, Mainz, Worms, and Speyer all have pretty spectacular cathedrals, and aren't so far as Cologne.