This info request is a bit o/t, but being from Cologne, I'll answer anyways.

The must-sees in Cologne are the Cathedral, one Romanesque church of your choosing, a stroll through the Altstadt, and Museum Ludwig, especially (on a first visit) for the Pop Art and Picasso in the permanent collection. All of these are in one walkable area and can be done on one (busy) day. Can-dos include more Romanesque churches, the Wallraf-Richartz museum, and the Chocolate museum (I would potentially bump up this recommendation depending on your child's age). If you're into cutting-edge art, check the Kunstverein and the galleries, Cologne (and Duesseldorf) is a massive hub for that stuff. But remember also that the charme of Cologne lies less in an abundance of 'must-see' things than in general quality of life. So just hang out. Window shopping might be interesting but with the current Euro, don't expect bargains at all.

If you're interested in a totally different facet of modern Germany, seek out Keupstrasse, the hub of Turkish Cologne. You'll also find outstanding Doener as well as Turkish sweets there. And you will have left the usual tourist path.

You seem to have three days, so you might want to use one day for day-tripping to either Bonn (a cute college town with many more old buildings standing than in Cologne and a completely oversized supply of high-brow culture due to its status as former capital) or Duesseldorf (for even more top-notch museums and the Medienhafen which is a showcase of contemporary architecture). The choice might depend on what's actually going on in the respective museums (K20, K21 for Duesseldorf, Bundeskunsthalle for Bonn). Both day trips can be done with public transportation, as can everything within the city.

If you would like to see a German village, timbered houses, rolling hills, that kind of stuff, day trip to Altenberg and its surroundings (< 1hr drive). Once there you can also hike, plus there's a major gothic cathedral. Any travel guide should contain info. This would require a car. Yet another alternative, especially with a kid, might be a boat trip down and up the Rhine; you can easily make it to just south of Bonn, where the river becomes very scenic and is lined with medieval fortresses (respectively their ruins).

Food: The region is extremely good for seriously upscale eating (I offhand know about 2 Michelin 3-stars, 3 2-stars, and a good handful of 1-stars) at comparatively (to France or even New York) bargain prices. If you're into that and your budget allows, do. You would absolutely have to make reservations in advance! For mid-price, if you speak German, the weekly restaurant reviews at the main local newspaper are a good source of inspiration. A personal recommendation is authentic Turkish food (more upscale than Doener sandwiches, but still very affordable) at Bosporus.
http://www.ksta.de/html/seiten/1097141168683/
Certainly one of the historic Brauhaeuser is a must, your guide will contain a list. At the truly budget level, one thing to try is Doener, which was pretty much invented in Germany's cities (as street food for Turkish workers).

Nightlife/bar life/music: is a major strength of Cologne, but choices really depend on your and your child's age.

Hope you'll enjoy your trip!