I spent a week in Düsseldorf every November for 13 years from 1996 to 2008 attending the Medica exhibition. The Altstadt is a great place for food and drink and as it should be waming up by then it will be more hospitable than in November.
You can't go to Düdo without trying the local specialities, Alt beer and Killepitsch. Visit the Killepitschstube "Et Kabüffke" in Flingerstrasse to try the local liqueur. It is so small they serve people out on the street through a window when it is full.
Food-wise there are several excellent German restaurants in the Altstadt. Many have their own microbrewery in house and make their own derivative of Alt beer. Goldener Kessel, Zum Schlüssel, Im Füchschen, Schweine Janes, Uerige Hausbrauerei, Schumacher... try the Schweinehaxe mit Apfelrotkohl und Klößen oder mit Sauerkraut und Kartoffelpüree (knuckle of grilled pork with red cabbage and potato dumpling or sauerkraut and mashed potatoes) or Rheinischer Sauerbraten in Rosinensauce, Apfelrotkohl, Kartoffelkloß, Mandelsplitter und Apfelmus (Rhine-style marinated beef with raisin sauce, red cabbage, potato dumpling and apple sauce).
If you are feeling brave, Schumacher and Uerige serve delicious Mettbrötchen which is raw minced pork with chopped onion and mustard, served on a bread roll. Even the sausages from the street vendors are better than anything you will find anywhere else.
In the same area are a few noisy pubs, notable ones are Da Speigel and Die Engel which is dark and dingy and plays very loud hard rock music. Look for the sign with the polar bear on!
For great views of the city go up the Rheinturm which has a revolving restaurant 180m above street level.
