Starting out with landbased fishing is not easy and also Wellington is not the easiest place to fish. You could get yourself a kayak and paddle out a few hundred meters into some of the sheltered bays. That would increase your chances of catching something dramatically.
What have you tried so far and what kind of gear do you have? Surfcasting can be quite good but requires a bit of patience, knowledge of the beach and the right bait. When landbased and fishing so close to shore your best times would be in the evening just before sunset. Try to find a day when the major or minor times are also around sunset to increase your chances.
Bait is also very important. If you're surfcasting off a beach try mussels or crabs or even store bought shrimps as bait.
If you're fishing in slightly deeper water off some rocks or around headlands, try to use berley to attract fish.
If you give me some pointers of what you have tried so far, I might be able to give a few more tips.
Ah thanks for the Kayak suggestion! I was thinking of getting one eventually.
My setup is pretty basic, I've got a 14 foot surf-casting rod and I've been using ledger rigs with breakaway sinkers, switching between single and double hook set ups. Lately I've been adding beads to the rig too. And for hooks I've been using 3/0 circle hooks so I don't have to worry about setting any bites, and can just chill on the beach with my rod in sitting in beach spike.
When I do go fishing I normally try to stay out for about 6 hours until the sunset and try get a change in tide, but I might need to get more particular about when I head out. I'll try line up some more major/minor times around sunset!
I suspect my bait choices have been an issue, I've been using pilchards & trevally from the petrol station, but they never seem very fresh. Not tried mussels, crabs or shrimp yet, so I'll definitely give those a go!
Most fish that come close to the beach are looking for food that you can find on the beach. So best to use mussels and crabs for bait. You could get a crab pot and try and catch a few paddle crabs for bait. Or look around some estuaries at low tide and see if you can collect some. They make great bait. As mussels and crabs are quite soft and easily fall off the hook it's best to make use of some bait elastic to secure your bait to the hook.