Once you are in Cologne you definitely have to visit the Cathedral (in German: Dom zu Koeln) - go inside and climb up the 509 stairs to the top of one of the towers and enjoy the great view from the top! Then walk through the old part of the city and along the Rhine river. In summer do a Rhine cruise and hop off at "Rheinaushafen" and walk around this area, which used to be an habour and is now becoming the "posh" area in Cologne with a great mixture of old and modern architecture.
When you are around in summer, you should definitely visit the "Flora" - the botanical garden of Cologne, which is really beautiful.
If you are into art, check out the Museum Ludwig right next to the Cathedral, where you can see a collection of 1960s Pop Art, German expressionism as well as Photography. If you are into (German) history visit the EL-DE Haus, which documents Cologne's Nazi era. But be aware that all museums in Cologne are closed on mondays!
In the evening you should check out the Zuelpicher Strasse - the student area - with a lot of nice (cocktail) bars and small clubs or Friesenstrasse. about 8 years ago