It should be worth mentioning that online casinos are accessible anywhere there’s internet because… they’re ONLINE. Having said that, though, I found that there are websites dedicated to helping Kiwis find good online casinos to play on, so you can probably start with those.
One that looks promising – at least in my opinion – is this website. It’s a site that compares online casinos catering to players from New Zealand. It could be worth looking into as you may find it more convenient to be able to spend local currency instead of USD or EUR while you play. Three months is a long time if you don’t find a way to entertain yourself, so playing online casino games to pass the time – and make a little more money while doing so – is a brilliant idea.