The "Schanzenviertel" (near Reeperbahn) has lots of independent llittle design shops. Perfect to get some nice cloths (Subway: "Feldstraße")

My favourite Hamburg Restaurant the the "Nil" (also in "Schanzenviertel") http://www.restaurant-nil.de/ (german only, sorry)
A small restaurant, located in an old shoe shop. Food is great and so is the service.

From Hamburg Harbour there is a Speedboat running to Helgoland which is a nice day trip, if you got some spare time left.