I've lived in Cologne for almost a decade, so I've figured out a few of the best places to eat. I tend to avoid expensive places, so all of my suggestions are suitable for more moderate budgets.
Disclaimer: My opinions may differ from yours.
Früh am Dom
Am Hof 12-14
Metro: Dom/Hauptbahnhof (multiple lines)
This is an outlet of one of Cologne's largest breweries. It has typical Cologne brewery food with typical Cologne brewery service. The waiters, here known as 'Köbes', are generally quite competent, but consider yourself warned about their strange sense of humor. The food is good and the prices are quite reasonable.
Am Weidenbach 24
Metro: Barbarossaplatz (multiple lines)
Weißbräu is another brewery, this time with a twist. Their specialty is Weißbier, which is something most of us know from the South of Germany. Despite the theme, the food here tends to be a little more typically from the Rhine (e.g Reibekuchen). The prices are quite fair, especially considering the large portions.
Zülpicher Str. 48
Metro: Dasslerstr./Bahnhof Süd (line 9)
The Magnus is located in the middle of the student quarter of the city. It's specialty is brunch on Sundays, which is always all-you-can-eat. It's a very good deal if you don't eat on Saturday. The restaurant is always crowded, so get there before you really *have* to eat.
Bei Oma Kleinmann
Zülpicher Str. 9
Metro: Zülpicherplatz (mulitple lines)
This is the place to go is you're looking for "real" German food. The restaurant's name can be translated as 'Grandma Kleinmann's Place' and all the food here is made by a real grandmother who is one of the best cooks in the city. All the food here is substantial and very reasonably priced.