I stayed in a hotel at the inner harbour last year. Each day I drove to the area were the Elbe-ferry once was situated, called Steubenhoft at the Albert Ballin Platz. Free parking space and you have a good view on the vessels coming from sea and from Hamburg. Close by is the old passenger terminal, now on level 2 (?) with a small restaurant, free museum and a free covered sitting area.
Across this quay is Alte Liebe, the wooden covered sitting area, also a good place to see the vessels passing but impossible to park your car (or very expensive). From this area also the harbour tour boats depart. The best in my opinion is the yellow STORTEBEKER: not so crowded and it goes also goes inside the industrial harbors.
I have never been to Kugelbake, seems a good spotting place as well, but parking seems difficult and far way from the water.
A nice day out was to the island Helgoland with the HELGOLAND: many vessels seen while underway.
Take a look first with Google Maps or Streetview.