Main shopping area in Hamburg is in the city centre with the Mönckebergstraße and the Spitalerstraße being the main streets with two major department stores and a huge electronic store. 

Just off the Mönckebergstraße there is the shopping centre "Europapassage" with dozens of shops.

North of the town hall/town hall market there are some high end shops as along the streets Jungfernstieg, Große Bleichen, Poststraße and the small shopping centres Hamburger Hof  and Hanseviertel. 

 

There are several other shopping centres and areas around Hamburg as in the North the huge Alstertal Einkaufzentrum (AEZ, S-Bahn station Poppenbüttel), in the East the shopping centre Wandsbek Quarree (U-Bahn station Wandsbek-Markt) and the Hamburger Meile (U-Bahn station Mundsburg or Hamburger Straße), in the West the Elbe Einkaufszentrum (EEZ, S-Bahn to Klein Flottbek, bus from there) and the Mercado shopping centre and the main shopping street Ottensener Hauptstraße in Altona and south of the Elbe river the Phoenix Center (S-Bahn station Harburg). 

For some more individual shopping there are some side streets in Altona, the areas of Eimsbüttel, WInterhude and Eppendorf having some unique shops. 

Hamburg Tourist Office - Shopping Info