In Cologne.

If you go into the Cathedral, make sure you see the ruins underneath the existing one.

For real, authentic Cologne, there are a couple of great pubs with good traditional food.
Everything is within walking distance of the Cathedral and Main Train Station.

Brauhaus Malzmühle (evenings best)
http://www.muehlenkoelsch.de/de/home.php
Wooden floors, walls, tables and chairs. Gemütlich halt.

Cölner Hofbräu Früh (Frühshoppen - Sunday morning breakfast - egg and bacon too! - with a glas of Kölsch - TRADITION)
http://www.frueh.de/
The architecture inside is not to be missed and the beer garden in front is great too.

For eating out, try the XII Apostel.
http://www.xii-apostel.com/12-apostel-koeln/koeln.html
Simply wonderful.

I've stayed in the Dom Hotel on business trips before. Not the best, but clean business hotel, good value for money (especially if you have to pay yourself), great breakfast and so central. In 3 minutes you can walk down to the old town and it's 2 minutes to the main train station.

Papa Joes Jazz Bar is a nice venue tight on the River for live music. Walking distance from the Chocolate Museum (great If your wife is with you) which is open Sundays too I believe.

Kölle Alaaf! (as the Rheinländer say)...