If you don´t want to discover Hamburg by bus or train – just take the waterway. It is cheaper as you might presume, because the tickets of „HADAG-Reederei“ and „Alstertouristik“ are integrated in the public transport system.
Alstertouristik
Alstertouristik offers a big variety of different tours to discover the city. You will find the descriptions at:
http://www.alstertouristik.de/e_index.php
HADAG-Reederei
“HADAG has been operating a scheduled boat service in Hamburg's docks for more than 115 years. Now HADAG is responsible for all ferry traffic in Hamburg docks in co-operation with HVV - a great opportunity to get to know the docks close up. Our Tolle Törns also offer a whole range of interesting tours along the Elbe both in and around Hamburg.”
http://www.hadag.de/e_index.php
Rainer Abicht Elbreederei
Rainer Abicht Elbreederei offers port tours and launch tours of the Warehouse City as well as private charters.