When I visit a town in Germany I've not visited before, I often try the 'Ratskeller' -- literally,…read morethe cellar of the town hall -- where there's nearly always (always?) a restaurant. For one thing, it's right in the town center, convenient to the town's sightseeing spots. But I've found most towns' Ratskellers are usually pretty good -- maybe not the finest restaurant in town, but definitely not the worst, and always full of local people. The Ratskeller in Luebeck is no exception.
Service was welcoming and cordial (for German standards) -- food was typical for the region and quite nice. We had herring in the 'housewife's style' (served chilled with onions & sour cream), and steamed cod. Both were high quality fish, nicely prepared. Just add beer and you've got a great lunch.