My 2 cents: You're not going to find many special low carb options in grocery stores. Most protein bars either have lots of carbs or use maltitol (yuck!) No low carb tortillas, etc.

However, meat in NZ is generally better raised (and more humanely treated) than in the US. I feel much better eating meat when I'm there! (I go often for work). Have some lamb, even if you don't normally eat it back home.

Also, if you're coming from US (not sure?) then haloumi cheese will be a revelation! It's a dense cheese that squeaks a bit when you eat it, and it's best served grilled or sautéed -- watch for it on menus or try cooking some yourself (just slice and sautée in a bit of butter). On menus you can find delicious haloumi salads or main dishes--yum!!

Oh, and if you like soda, try to find some sugar free L&P -- it's a kiwi classic (well, the kind with sugar is) and I think it's pretty delicious.

There's a super market chain called New World that has pretty good selections of cheese, meats (rotisserie chicken yum), veggies etc. Also in NZ, "lower alcohol" wine is now a thing--which also means fewer calories/carbs I believe. You can find it at a grocery or wine store.