If you are in the middle of the city and wanna treat yourself, go where the merchants go: Casse-Croûte.
It is a cosy French-German bistro and restaurant nearby Gänsemarkt and the Opera house. A little hidden in a small street, you can find this gem which serves high-class food like oysters, very decent bouillabaisse and typical Northern German dishes. Among these are some classics like Königsberger Klopse (big meatballs served with white caper sauce) and Labskaus (THE Hamburg dish, a mixture of meat and mashed potatoes with gherkin).
There is a quirky and lively atmosphere inside, and especially during the winter, I love the cosiness and quality of the place which matches the friendly staff. When I want to spend some money on good food, I like to come and eat here. Well, the wines are good too.