Port Gellibrand Coastal Heritage Park at Williamstown (visible behind the oil tanks) is a good location for shipspotting in Melbourne.
It gives a good, close view of all ships entering or leaving Melbourne, whether they are going up into the Yarra River or outside to the Webb Dock or Princes Pier.
It's easy to take photos like this: http://www.shipspotting.com/gallery/photo.php?lid=2573260
There are park benches right at the water's edge and plenty of parking.
Just three blocks walk from the cafes on the main street or even closer if you come by train to Williamstown Station.
If you are visiting Melbourne, a ferry trip from Southbank takes you past the port areas in the river giving close-up views of plenty of shipping activity too like these:
http://www.shipspotting.com/gallery/photo.php?lid=2573264
http://www.shipspotting.com/gallery/photo.php?lid=2573266