Do a harbour cruise "Hafenrundfahrt" that will take you through the "Speicherstadt", the old part of the harbour with the old warehouses which have been beutifully restored.

There are also some good museums "Hamburger Kunsthalle" "Museum fuer Kunst und Gewerbe"

Stroll along the Alster lake and shop in the fancy arcades near Jungfernstieg and Gaensemarkt.

Enjoy a seafood meal in Finkenwerder (a subburb at the river Elbe) and look at the cottages of retired sea captains.

As an FT'er a must should be a visit to the Airbus plant. IIRC the plant is open to the public at least on weekdays. You might be lucky and see the odd Airbus Beluga take off transporting wings or other large Airbus parts to France.

In the evening enjoy a musical or concert in one of the many theatres or is so inclinde visit the Reperbahn....the famous red-light district near the harbour.

Plenty to do in that wonderful city.

Enjoy!