Sea fishing around Dunedin is quite limited compared to the far north.
the harbour is OK for salmon during the summer months. They also get the occasional blue cod (generally undersized)
Better fishing around the Otago peninsula for cod and Moki but Access can be an issue off rocks unless you have a boat. Quite a few sharks are taken of Tairoa head and puddingstone but again access is an issue. There is good fishing for Trout flounder and kahawai at the Taeri river mouth if your into that. But In my opinion the best surf fishing is off the shingle beaches north of Dunedin around Oamaru/hampden where the species are similar to Canterbury in the warmer mouths they get Rig, Elephant fish and various other sharks.