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.
Outram Glen(Taieri river at the start of the gorge) has a lot of small trout but have seen and caught a 3lb brown in the swimming hole after swimmers have gone. Was back in February and just before dusk on a hares ear nymph. Nothing much doing now though. Sullivans dam just off the northern motorway has rainbows and browns, but Iv been trying my luck with a spinner in the harbour at the Leith mouth, no luck so far.