My family is from Hamburg. Here are some restaurants which come to mind. Most of them are nicer places where we have had "celebrations" or the like.

• Hotel Jacobs, out on the Elbe
• Haerlin, in the Vierjahreszeiten
• Hotel Atlantic (our family's main stay for about 50 years )
• the restaurant up on the Sullberg -- can;t remember the name
• Landhaus Scherrer
• Friesen Keller (down at the water level, one block in front of city hall [Rathaus])
• Eichtal out in Wandsbek
• Fisherreihafen Hamburg
• Sunday brunch -- you have to go to the fish market!!!
• Hotel Hafen Hamburg -- if the weather is nice, overlooks the whole harbor
• Tschebull - Austrian/South German food
• East
• Faehrhaus Oevelgoenne
• Carls (or Karls?)
• there's a new modern restaurant down on the Elbe. The chef also has a TV show. I can't remember his name, but when we were in Hamburg last spring, everyone knew about it. Something like Tafelhaus.
• if you like watching the ships come into harbor, go up-river to Faehrhaus Willkomm Hoeft (spelling?); easy walking from the S-bhan station Wedel. Go in good weather. They welcome each ship with that ship's national anthem, report on the stats of the ship, where is is coming from, etc. Upon departure, they give a grand send off, etc.