Although Maori have their own culinary tradition (of which we had no chance to try as we visited southern parts of the South Island), the food that is eaten by the Kiwis of European origins appeared to be along the lines of traditional English food. With our CouchSurfing hosts we had basic roast lamb, boiled corned beef (corned beef here being cured beef, not the tinned mushy stuff that goes into horrid sandwiches in the UK) and pork hot pot (as well as amazing purple soup, made with purple sweet potatoes, but this was in a vegetarian multi-national student household so doesn't really count). When staying in paid accommodation, we self catered a lot, and when not doing that we pretty much lived on fish and chips (though we had some other food occasionally, including surprisingly decent Indian meals in Christchurch and Dunedin).
There is a LOT of fish and chips around in New Zealand. The place is surrounded by sea, so eating fish is an obvious thing, though surprising proportion of fish is apparently from frozen. There is usually a selection of different types of fish, and standard condiments include sauce tartare and ketchup (you pay extra for those). It's still pretty good value meal in New Zealand: we paid as little as 5 NZD for fish-and-chips (that is 2.50 GBP, unheard of in the UK), though a standard price is closer to 10 NZD (which is still reasonable value, as you usually, just like in the UK, get a lot).
The best (though not the cheapest) fish and chips we had in our month in New Zealand were undoubtedly from a Queenstown chippie called Aggy's Shack (see a review). I am not sure if it was the best fish and chips I ever had (we do live, after all, within an hour's drive from a few places claiming to sell the best fish suppers in the land) but easily a contender.
Interesting native or local foods didn't register on our radar in New Zealand, apart from the aforementioned purple sweet potato (sweet potato, known locally by its Maori name of kumara, is a very popular vegetable in New Zealand). Local drinks include a rich array of New Zealand wine, of which we sampled some interesting varieties when passing through Central Otago, world's most southerly wine producing region. Although New Zealand is known mostly for its whites, Central Otago produces reds, 85% of which are Pinot Noir which certainly merits attention, we sampled pretty amazing stuff from Gibbston Valley but there are many wineries to explore and what they produce is often very far off the ''big, fruity, bold, easy'' stereotype of a New World wine.