Hop on Ferry 62 at Landungsbrücken (Bridge 3) and take a ride to Finkenwerder and back (you don't even have to get off there). You will have a great view of the port on one side of the river and the beach on the other. Located about halfway between Övelgönne and Finkenwerde Stations you'll see a huge stone on the beach - the old Swede ("Alter Schwede") - considered the first immigrant to Hamburg: It came on a glacier in the last ice age. You'll also see the old fish auction hall ("Fischauktionshalle") and plenty of fancy new buildings before you reach the beach.
The ride back and forth taktes about 50 Minutes. Ferries run every 20 Minutes (Schedule: http://www.hadag.de/fahrplan-pdf/62_rueck.pdf). It is very cheap, too - public transportation fees apply. So if you buy a ticket for the day the ride is included.